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example_30000_combination_6
\documentclass[reqno,fleqn]{amsart} \usepackage{amsfonts,amsthm,amssymb} \usepackage[utf8]{inputenc} \usepackage{amssymb} \usepackage{amsmath} \usepackage{tikz} \usepackage{amsmath} \usepackage{tikz} \usetikzlibrary{positioning} \begin{document} \begin{tikzpicture}[thick, set/.style = { circle, minimum size = .061cm}] \draw[green] (3,0) ellipse (2cm and 1cm); \draw[blue] (1,0) ellipse (1.94cm and 0.99cm); \begin{scope}[red] \clip(2,-1)rectangle(3,1.2); \draw (1,0) circle [x radius=2cm, y radius=10mm]; \end{scope} \begin{scope}[red] \clip(2,-1)rectangle(3,1.2); \draw (1,0) circle [x radius=1.975cm, y radius=10mm]; \end{scope} \begin{scope}[blue] \clip(2,-1)rectangle(3,1.2); \draw (1,0) circle [x radius=1.935cm, y radius=9.8mm]; \end{scope} \begin{scope}[red] \clip(2,-1.5)rectangle(7,1.5); \draw (4,0) circle [x radius=3cm, y radius=11.9mm]; \end{scope} \node[blue] at (0,0) {$N_{i}\setminus N_{i+1}$}; \end{tikzpicture} \end{document}
example_30000_combination_1
\documentclass[reqno,fleqn]{amsart} \usepackage{amsfonts,amsthm,amssymb} \usepackage[utf8]{inputenc} \usepackage{amssymb} \usepackage{amsmath} \usepackage{tikz} \usepackage{amsmath} \usepackage{tikz} \usetikzlibrary{positioning} \begin{document} \begin{tikzpicture}[thick, set/.style = { circle, minimum size = .061cm}] \draw[green] (3,0) ellipse (2cm and 1cm); \end{tikzpicture} \end{document}
example_30000_combination_8
\documentclass[reqno,fleqn]{amsart} \usepackage{amsfonts,amsthm,amssymb} \usepackage[utf8]{inputenc} \usepackage{amssymb} \usepackage{amsmath} \usepackage{tikz} \usepackage{amsmath} \usepackage{tikz} \usetikzlibrary{positioning} \begin{document} \begin{tikzpicture}[thick, set/.style = { circle, minimum size = .061cm}] \draw[green] (3,0) ellipse (2cm and 1cm); \draw[blue] (1,0) ellipse (1.94cm and 0.99cm); \begin{scope}[red] \clip(2,-1)rectangle(3,1.2); \draw (1,0) circle [x radius=2cm, y radius=10mm]; \end{scope} \begin{scope}[red] \clip(2,-1)rectangle(3,1.2); \draw (1,0) circle [x radius=1.975cm, y radius=10mm]; \end{scope} \begin{scope}[blue] \clip(2,-1)rectangle(3,1.2); \draw (1,0) circle [x radius=1.935cm, y radius=9.8mm]; \end{scope} \begin{scope}[red] \clip(2,-1.5)rectangle(7,1.5); \draw (4,0) circle [x radius=3cm, y radius=11.9mm]; \end{scope} \node[blue] at (0,0) {$N_{i}\setminus N_{i+1}$}; \node at (2,0) {\tiny $N_{i}\cap N_{i+1}$}; \node[green] at (4,0.2) {$N_{i+1}\setminus N_{i}$}; \end{tikzpicture} \end{document}
example_30000_combination_9
\documentclass[reqno,fleqn]{amsart} \usepackage{amsfonts,amsthm,amssymb} \usepackage[utf8]{inputenc} \usepackage{amssymb} \usepackage{amsmath} \usepackage{tikz} \usepackage{amsmath} \usepackage{tikz} \usetikzlibrary{positioning} \begin{document} \begin{tikzpicture}[thick, set/.style = { circle, minimum size = .061cm}] \draw[green] (3,0) ellipse (2cm and 1cm); \draw[blue] (1,0) ellipse (1.94cm and 0.99cm); \begin{scope}[red] \clip(2,-1)rectangle(3,1.2); \draw (1,0) circle [x radius=2cm, y radius=10mm]; \end{scope} \begin{scope}[red] \clip(2,-1)rectangle(3,1.2); \draw (1,0) circle [x radius=1.975cm, y radius=10mm]; \end{scope} \begin{scope}[blue] \clip(2,-1)rectangle(3,1.2); \draw (1,0) circle [x radius=1.935cm, y radius=9.8mm]; \end{scope} \begin{scope}[red] \clip(2,-1.5)rectangle(7,1.5); \draw (4,0) circle [x radius=3cm, y radius=11.9mm]; \end{scope} \node[blue] at (0,0) {$N_{i}\setminus N_{i+1}$}; \node at (2,0) {\tiny $N_{i}\cap N_{i+1}$}; \node[green] at (4,0.2) {$N_{i+1}\setminus N_{i}$}; \node[red] at (6,-0.2) {$N_{i+2}\setminus N_{i+1}$}; \end{tikzpicture} \end{document}
example_30000_combination_7
\documentclass[reqno,fleqn]{amsart} \usepackage{amsfonts,amsthm,amssymb} \usepackage[utf8]{inputenc} \usepackage{amssymb} \usepackage{amsmath} \usepackage{tikz} \usepackage{amsmath} \usepackage{tikz} \usetikzlibrary{positioning} \begin{document} \begin{tikzpicture}[thick, set/.style = { circle, minimum size = .061cm}] \draw[green] (3,0) ellipse (2cm and 1cm); \draw[blue] (1,0) ellipse (1.94cm and 0.99cm); \begin{scope}[red] \clip(2,-1)rectangle(3,1.2); \draw (1,0) circle [x radius=2cm, y radius=10mm]; \end{scope} \begin{scope}[red] \clip(2,-1)rectangle(3,1.2); \draw (1,0) circle [x radius=1.975cm, y radius=10mm]; \end{scope} \begin{scope}[blue] \clip(2,-1)rectangle(3,1.2); \draw (1,0) circle [x radius=1.935cm, y radius=9.8mm]; \end{scope} \begin{scope}[red] \clip(2,-1.5)rectangle(7,1.5); \draw (4,0) circle [x radius=3cm, y radius=11.9mm]; \end{scope} \node[blue] at (0,0) {$N_{i}\setminus N_{i+1}$}; \node at (2,0) {\tiny $N_{i}\cap N_{i+1}$}; \end{tikzpicture} \end{document}
example_30000_combination_4
\documentclass[reqno,fleqn]{amsart} \usepackage{amsfonts,amsthm,amssymb} \usepackage[utf8]{inputenc} \usepackage{amssymb} \usepackage{amsmath} \usepackage{tikz} \usepackage{amsmath} \usepackage{tikz} \usetikzlibrary{positioning} \begin{document} \begin{tikzpicture}[thick, set/.style = { circle, minimum size = .061cm}] \draw[green] (3,0) ellipse (2cm and 1cm); \draw[blue] (1,0) ellipse (1.94cm and 0.99cm); \begin{scope}[red] \clip(2,-1)rectangle(3,1.2); \draw (1,0) circle [x radius=2cm, y radius=10mm]; \end{scope} \begin{scope}[red] \clip(2,-1)rectangle(3,1.2); \draw (1,0) circle [x radius=1.975cm, y radius=10mm]; \end{scope} \begin{scope}[blue] \clip(2,-1)rectangle(3,1.2); \draw (1,0) circle [x radius=1.935cm, y radius=9.8mm]; \end{scope} \end{tikzpicture} \end{document}
example_30000_combination_3
\documentclass[reqno,fleqn]{amsart} \usepackage{amsfonts,amsthm,amssymb} \usepackage[utf8]{inputenc} \usepackage{amssymb} \usepackage{amsmath} \usepackage{tikz} \usepackage{amsmath} \usepackage{tikz} \usetikzlibrary{positioning} \begin{document} \begin{tikzpicture}[thick, set/.style = { circle, minimum size = .061cm}] \draw[green] (3,0) ellipse (2cm and 1cm); \draw[blue] (1,0) ellipse (1.94cm and 0.99cm); \begin{scope}[red] \clip(2,-1)rectangle(3,1.2); \draw (1,0) circle [x radius=2cm, y radius=10mm]; \end{scope} \end{tikzpicture} \end{document}
example_30000_combination_2
\documentclass[reqno,fleqn]{amsart} \usepackage{amsfonts,amsthm,amssymb} \usepackage[utf8]{inputenc} \usepackage{amssymb} \usepackage{amsmath} \usepackage{tikz} \usepackage{amsmath} \usepackage{tikz} \usetikzlibrary{positioning} \begin{document} \begin{tikzpicture}[thick, set/.style = { circle, minimum size = .061cm}] \draw[green] (3,0) ellipse (2cm and 1cm); \draw[blue] (1,0) ellipse (1.94cm and 0.99cm); \end{tikzpicture} \end{document}
example_30000_combination_5
\documentclass[reqno,fleqn]{amsart} \usepackage{amsfonts,amsthm,amssymb} \usepackage[utf8]{inputenc} \usepackage{amssymb} \usepackage{amsmath} \usepackage{tikz} \usepackage{amsmath} \usepackage{tikz} \usetikzlibrary{positioning} \begin{document} \begin{tikzpicture}[thick, set/.style = { circle, minimum size = .061cm}] \draw[green] (3,0) ellipse (2cm and 1cm); \draw[blue] (1,0) ellipse (1.94cm and 0.99cm); \begin{scope}[red] \clip(2,-1)rectangle(3,1.2); \draw (1,0) circle [x radius=2cm, y radius=10mm]; \end{scope} \begin{scope}[red] \clip(2,-1)rectangle(3,1.2); \draw (1,0) circle [x radius=1.975cm, y radius=10mm]; \end{scope} \begin{scope}[blue] \clip(2,-1)rectangle(3,1.2); \draw (1,0) circle [x radius=1.935cm, y radius=9.8mm]; \end{scope} \begin{scope}[red] \clip(2,-1.5)rectangle(7,1.5); \draw (4,0) circle [x radius=3cm, y radius=11.9mm]; \end{scope} \end{tikzpicture} \end{document}
example_30000_combination_10
\documentclass[reqno,fleqn]{amsart} \usepackage{amsfonts,amsthm,amssymb} \usepackage[utf8]{inputenc} \usepackage{amssymb} \usepackage{amsmath} \usepackage{tikz} \usepackage{amsmath} \usepackage{tikz} \usetikzlibrary{positioning} \begin{document} \begin{tikzpicture}[thick, set/.style = { circle, minimum size = .061cm}] \draw[green] (3,0) ellipse (2cm and 1cm); \draw[blue] (1,0) ellipse (1.94cm and 0.99cm); \begin{scope}[red] \clip(2,-1)rectangle(3,1.2); \draw (1,0) circle [x radius=2cm, y radius=10mm]; \end{scope} \begin{scope}[red] \clip(2,-1)rectangle(3,1.2); \draw (1,0) circle [x radius=1.975cm, y radius=10mm]; \end{scope} \begin{scope}[blue] \clip(2,-1)rectangle(3,1.2); \draw (1,0) circle [x radius=1.935cm, y radius=9.8mm]; \end{scope} \begin{scope}[red] \clip(2,-1.5)rectangle(7,1.5); \draw (4,0) circle [x radius=3cm, y radius=11.9mm]; \end{scope} \node[blue] at (0,0) {$N_{i}\setminus N_{i+1}$}; \node at (2,0) {\tiny $N_{i}\cap N_{i+1}$}; \node[green] at (4,0.2) {$N_{i+1}\setminus N_{i}$}; \node[red] at (6,-0.2) {$N_{i+2}\setminus N_{i+1}$}; \end{tikzpicture} \end{document}
example_30000_main
\documentclass[reqno,fleqn]{amsart} \usepackage{amsfonts,amsthm,amssymb} \usepackage[utf8]{inputenc} \usepackage{amssymb} \usepackage{amsmath} \usepackage{tikz} \usepackage{amsmath} \usepackage{tikz} \usetikzlibrary{positioning} \begin{document} \begin{tikzpicture}[thick, set/.style = { circle, minimum size = .061cm}] \draw[green] (3,0) ellipse (2cm and 1cm); \draw[blue] (1,0) ellipse (1.94cm and 0.99cm); \begin{scope}[red] \clip(2,-1)rectangle(3,1.2); \draw (1,0) circle [x radius=2cm, y radius=10mm]; \end{scope} \begin{scope}[red] \clip(2,-1)rectangle(3,1.2); \draw (1,0) circle [x radius=1.975cm, y radius=10mm]; \end{scope} \begin{scope}[blue] \clip(2,-1)rectangle(3,1.2); \draw (1,0) circle [x radius=1.935cm, y radius=9.8mm]; \end{scope} \begin{scope}[red] \clip(2,-1.5)rectangle(7,1.5); \draw (4,0) circle [x radius=3cm, y radius=11.9mm]; \end{scope} \node[blue] at (0,0) {$N_{i}\setminus N_{i+1}$}; \node at (2,0) {\tiny $N_{i}\cap N_{i+1}$}; \node[green] at (4,0.2) {$N_{i+1}\setminus N_{i}$}; \node[red] at (6,-0.2) {$N_{i+2}\setminus N_{i+1}$}; \end{tikzpicture} \end{document}
example_30001_combination_2
\documentclass[11pt]{amsart} \usepackage{amsmath,amsthm,amssymb,amsfonts,amscd} \usepackage{tikz-cd} \usepackage[latin2]{inputenc} \usetikzlibrary{matrix} \tikzcdset{scale cd/.style={every label/.append style={scale=#1}, cells={nodes={scale=#1}}}} \begin{document} \begin{tikzpicture} \draw (0, 0) node[below]{{\footnotesize{$y_{2n+1}$}}}; \draw (1,0) node[below]{{\footnotesize{$y_{2n+3}$}}}; \draw (2,0) node[below]{{\footnotesize{$y_{2n+5}$}}}; \draw (3,0) node[below]{{\footnotesize{$y_{2n+7}$}}}; \draw (4,0) node[below]{{\footnotesize{$y_{2n+9}$}}}; \draw (2, 0) arc (45:135:1.41cm); \draw (3, 0) arc (-45:-135:1.41cm); \end{tikzpicture} \end{document}
example_30001_combination_3
\documentclass[11pt]{amsart} \usepackage{amsmath,amsthm,amssymb,amsfonts,amscd} \usepackage{tikz-cd} \usepackage[latin2]{inputenc} \usetikzlibrary{matrix} \tikzcdset{scale cd/.style={every label/.append style={scale=#1}, cells={nodes={scale=#1}}}} \begin{document} \begin{tikzpicture} \draw (0, 0) node[below]{{\footnotesize{$y_{2n+1}$}}}; \draw (1,0) node[below]{{\footnotesize{$y_{2n+3}$}}}; \draw (2,0) node[below]{{\footnotesize{$y_{2n+5}$}}}; \draw (3,0) node[below]{{\footnotesize{$y_{2n+7}$}}}; \draw (4,0) node[below]{{\footnotesize{$y_{2n+9}$}}}; \draw (2, 0) arc (45:135:1.41cm); \draw (3, 0) arc (-45:-135:1.41cm); \end{tikzpicture} \end{document}
example_30001_combination_1
\documentclass[11pt]{amsart} \usepackage{amsmath,amsthm,amssymb,amsfonts,amscd} \usepackage{tikz-cd} \usepackage[latin2]{inputenc} \usetikzlibrary{matrix} \tikzcdset{scale cd/.style={every label/.append style={scale=#1}, cells={nodes={scale=#1}}}} \begin{document} \begin{tikzpicture} \draw (0, 0) node[below]{{\footnotesize{$y_{2n+1}$}}}; \draw (1,0) node[below]{{\footnotesize{$y_{2n+3}$}}}; \draw (2,0) node[below]{{\footnotesize{$y_{2n+5}$}}}; \draw (3,0) node[below]{{\footnotesize{$y_{2n+7}$}}}; \draw (4,0) node[below]{{\footnotesize{$y_{2n+9}$}}}; \end{tikzpicture} \end{document}
example_30001_main
\documentclass[11pt]{amsart} \usepackage{amsmath,amsthm,amssymb,amsfonts,amscd} \usepackage{tikz-cd} \usepackage[latin2]{inputenc} \usetikzlibrary{matrix} \tikzcdset{scale cd/.style={every label/.append style={scale=#1}, cells={nodes={scale=#1}}}} \begin{document} \begin{tikzpicture} \draw (0, 0) node[below]{{\footnotesize{$y_{2n+1}$}}}; \draw (1,0) node[below]{{\footnotesize{$y_{2n+3}$}}}; \draw (2,0) node[below]{{\footnotesize{$y_{2n+5}$}}}; \draw (3,0) node[below]{{\footnotesize{$y_{2n+7}$}}}; \draw (4,0) node[below]{{\footnotesize{$y_{2n+9}$}}}; \draw (2, 0) arc (45:135:1.41cm); \draw (3, 0) arc (-45:-135:1.41cm); \end{tikzpicture} \end{document}
example_30002_combination_1
\documentclass[11pt]{amsart} \usepackage{amsmath,amsthm,amssymb,amsfonts,amscd} \usepackage{tikz-cd} \usepackage[latin2]{inputenc} \usetikzlibrary{matrix} \tikzcdset{scale cd/.style={every label/.append style={scale=#1}, cells={nodes={scale=#1}}}} \begin{document} \begin{tikzpicture} \draw (0, 0) node[below]{{\footnotesize{$y_{2n+1}$}}}; \draw (1,0) node[below]{{\footnotesize{$y_{2n+3}$}}}; \draw (2,0) node[below]{{\footnotesize{$y_{2n+5}$}}}; \draw (3,0) node[below]{{\footnotesize{$y_{2n+7}$}}}; \draw (4,0) node[below]{{\footnotesize{$y_{2n+9}$}}}; \end{tikzpicture} \end{document}
example_30002_combination_2
\documentclass[11pt]{amsart} \usepackage{amsmath,amsthm,amssymb,amsfonts,amscd} \usepackage{tikz-cd} \usepackage[latin2]{inputenc} \usetikzlibrary{matrix} \tikzcdset{scale cd/.style={every label/.append style={scale=#1}, cells={nodes={scale=#1}}}} \begin{document} \begin{tikzpicture} \draw (0, 0) node[below]{{\footnotesize{$y_{2n+1}$}}}; \draw (1,0) node[below]{{\footnotesize{$y_{2n+3}$}}}; \draw (2,0) node[below]{{\footnotesize{$y_{2n+5}$}}}; \draw (3,0) node[below]{{\footnotesize{$y_{2n+7}$}}}; \draw (4,0) node[below]{{\footnotesize{$y_{2n+9}$}}}; \draw (2, 0) arc (-45:-135:1.41cm); \draw (4, 0) arc (45:135:1.41cm); \end{tikzpicture} \end{document}
example_30002_combination_3
\documentclass[11pt]{amsart} \usepackage{amsmath,amsthm,amssymb,amsfonts,amscd} \usepackage{tikz-cd} \usepackage[latin2]{inputenc} \usetikzlibrary{matrix} \tikzcdset{scale cd/.style={every label/.append style={scale=#1}, cells={nodes={scale=#1}}}} \begin{document} \begin{tikzpicture} \draw (0, 0) node[below]{{\footnotesize{$y_{2n+1}$}}}; \draw (1,0) node[below]{{\footnotesize{$y_{2n+3}$}}}; \draw (2,0) node[below]{{\footnotesize{$y_{2n+5}$}}}; \draw (3,0) node[below]{{\footnotesize{$y_{2n+7}$}}}; \draw (4,0) node[below]{{\footnotesize{$y_{2n+9}$}}}; \draw (2, 0) arc (-45:-135:1.41cm); \draw (4, 0) arc (45:135:1.41cm); \end{tikzpicture} \end{document}
example_30002_main
\documentclass[11pt]{amsart} \usepackage{amsmath,amsthm,amssymb,amsfonts,amscd} \usepackage{tikz-cd} \usepackage[latin2]{inputenc} \usetikzlibrary{matrix} \tikzcdset{scale cd/.style={every label/.append style={scale=#1}, cells={nodes={scale=#1}}}} \begin{document} \begin{tikzpicture} \draw (0, 0) node[below]{{\footnotesize{$y_{2n+1}$}}}; \draw (1,0) node[below]{{\footnotesize{$y_{2n+3}$}}}; \draw (2,0) node[below]{{\footnotesize{$y_{2n+5}$}}}; \draw (3,0) node[below]{{\footnotesize{$y_{2n+7}$}}}; \draw (4,0) node[below]{{\footnotesize{$y_{2n+9}$}}}; \draw (2, 0) arc (-45:-135:1.41cm); \draw (4, 0) arc (45:135:1.41cm); \end{tikzpicture} \end{document}
example_30003_combination_2
\documentclass[a4paper,11pt]{article} \usepackage[T1]{fontenc} \usepackage[utf8]{inputenc} \usepackage{amsmath} \usepackage{amsmath} \usepackage{amssymb} \usepackage[colorinlistoftodos]{todonotes} \usepackage{tikz} \begin{document} \begin{tikzpicture} \draw (2,2) ellipse (1cm and 2cm); \draw (14,2) ellipse (1cm and 2cm); \end{tikzpicture} \end{document}
example_30003_combination_5
\documentclass[a4paper,11pt]{article} \usepackage[T1]{fontenc} \usepackage[utf8]{inputenc} \usepackage{amsmath} \usepackage{amsmath} \usepackage{amssymb} \usepackage[colorinlistoftodos]{todonotes} \usepackage{tikz} \begin{document} \begin{tikzpicture} \draw (2,2) ellipse (1cm and 2cm); \draw (14,2) ellipse (1cm and 2cm); \draw (2.2,3.95) .. controls (8,2) .. (13.8,3.95); \draw (2.2,0.05) .. controls (8,2) .. (13.8,0.05); \draw (8,2) circle (0.5cm); \end{tikzpicture} \end{document}
example_30003_combination_4
\documentclass[a4paper,11pt]{article} \usepackage[T1]{fontenc} \usepackage[utf8]{inputenc} \usepackage{amsmath} \usepackage{amsmath} \usepackage{amssymb} \usepackage[colorinlistoftodos]{todonotes} \usepackage{tikz} \begin{document} \begin{tikzpicture} \draw (2,2) ellipse (1cm and 2cm); \draw (14,2) ellipse (1cm and 2cm); \draw (2.2,3.95) .. controls (8,2) .. (13.8,3.95); \draw (2.2,0.05) .. controls (8,2) .. (13.8,0.05); \end{tikzpicture} \end{document}
example_30003_combination_3
\documentclass[a4paper,11pt]{article} \usepackage[T1]{fontenc} \usepackage[utf8]{inputenc} \usepackage{amsmath} \usepackage{amsmath} \usepackage{amssymb} \usepackage[colorinlistoftodos]{todonotes} \usepackage{tikz} \begin{document} \begin{tikzpicture} \draw (2,2) ellipse (1cm and 2cm); \draw (14,2) ellipse (1cm and 2cm); \draw (2.2,3.95) .. controls (8,2) .. (13.8,3.95); \end{tikzpicture} \end{document}
example_30003_combination_7
\documentclass[a4paper,11pt]{article} \usepackage[T1]{fontenc} \usepackage[utf8]{inputenc} \usepackage{amsmath} \usepackage{amsmath} \usepackage{amssymb} \usepackage[colorinlistoftodos]{todonotes} \usepackage{tikz} \begin{document} \begin{tikzpicture} \draw (2,2) ellipse (1cm and 2cm); \draw (14,2) ellipse (1cm and 2cm); \draw (2.2,3.95) .. controls (8,2) .. (13.8,3.95); \draw (2.2,0.05) .. controls (8,2) .. (13.8,0.05); \draw (8,2) circle (0.5cm); \node[draw] at (2,-1) {Antiuniverse}; \node[draw] at (14,-1) {Universe}; \end{tikzpicture} \end{document}
example_30003_combination_6
\documentclass[a4paper,11pt]{article} \usepackage[T1]{fontenc} \usepackage[utf8]{inputenc} \usepackage{amsmath} \usepackage{amsmath} \usepackage{amssymb} \usepackage[colorinlistoftodos]{todonotes} \usepackage{tikz} \begin{document} \begin{tikzpicture} \draw (2,2) ellipse (1cm and 2cm); \draw (14,2) ellipse (1cm and 2cm); \draw (2.2,3.95) .. controls (8,2) .. (13.8,3.95); \draw (2.2,0.05) .. controls (8,2) .. (13.8,0.05); \draw (8,2) circle (0.5cm); \node[draw] at (2,-1) {Antiuniverse}; \end{tikzpicture} \end{document}
example_30003_combination_1
\documentclass[a4paper,11pt]{article} \usepackage[T1]{fontenc} \usepackage[utf8]{inputenc} \usepackage{amsmath} \usepackage{amsmath} \usepackage{amssymb} \usepackage[colorinlistoftodos]{todonotes} \usepackage{tikz} \begin{document} \begin{tikzpicture} \draw (2,2) ellipse (1cm and 2cm); \end{tikzpicture} \end{document}
example_30003_combination_8
\documentclass[a4paper,11pt]{article} \usepackage[T1]{fontenc} \usepackage[utf8]{inputenc} \usepackage{amsmath} \usepackage{amsmath} \usepackage{amssymb} \usepackage[colorinlistoftodos]{todonotes} \usepackage{tikz} \begin{document} \begin{tikzpicture} \draw (2,2) ellipse (1cm and 2cm); \draw (14,2) ellipse (1cm and 2cm); \draw (2.2,3.95) .. controls (8,2) .. (13.8,3.95); \draw (2.2,0.05) .. controls (8,2) .. (13.8,0.05); \draw (8,2) circle (0.5cm); \node[draw] at (2,-1) {Antiuniverse}; \node[draw] at (14,-1) {Universe}; \node[draw] at (8,3.5) {Big bang singularity}; \end{tikzpicture} \end{document}
example_30003_main
\documentclass[a4paper,11pt]{article} \usepackage[T1]{fontenc} \usepackage[utf8]{inputenc} \usepackage{amsmath} \usepackage{amsmath} \usepackage{amssymb} \usepackage[colorinlistoftodos]{todonotes} \usepackage{tikz} \begin{document} \begin{tikzpicture} \draw (2,2) ellipse (1cm and 2cm); \draw (14,2) ellipse (1cm and 2cm); \draw (2.2,3.95) .. controls (8,2) .. (13.8,3.95); \draw (2.2,0.05) .. controls (8,2) .. (13.8,0.05); \draw (8,2) circle (0.5cm); \node[draw] at (2,-1) {Antiuniverse}; \node[draw] at (14,-1) {Universe}; \node[draw] at (8,3.5) {Big bang singularity}; \end{tikzpicture} \end{document}
example_30004_combination_5
\documentclass[12pt, a4paper]{elsarticle} \usepackage{amssymb} \usepackage{tikz} \usepackage{amsmath} \usepackage{xcolor} \usepackage{pgf} \usetikzlibrary{ matrix, shapes, arrows, shadows, calc, chains, decorations.pathmorphing, decorations.text, arrows.meta, patterns, fit, bending, shadows, shapes.geometric, snakes } \tikzset{ label/.style={ font=\scriptsize\itshape, inner sep=0.4em }, point/.style={ circle, fill=black, text width=0.3em, inner sep=0 }, state/.style={ circle, text width=0.8em, inner sep=0.1em, text depth=0.08em, draw, font=\scriptsize }, participant/.style={ draw=black, rounded corners, semithick, font=\footnotesize, text height=0.2cm, % minimum height=0.5cm, text centered, anchor=base }, specification/.style={ font=\small, semithick, draw=black }, synthesiser/.style={ draw=black, dotted, semithick, inner sep=2pt, font=\footnotesize }, monitor/.style={ % rounded corners=1mm, draw=black, fill=white, semithick, minimum width=0.5cm, minimum height=0.5cm, font=\footnotesize, text height=0.2cm, drop shadow=ashadow }, point/.style={ minimum size=0pt, inner sep=0pt }, ltspoint/.style={ circle, fill=black, draw=white, line width=0.5mm, text width=0.25em, inner sep=0, font=\footnotesize }, ashadow/.style={ opacity=.3, shadow xshift=0.6mm, shadow yshift=-0.6mm }, oppashadow/.style={ opacity=.3, shadow xshift=-0.6mm, shadow yshift=-0.6mm }, process/.style={ draw=black, fill=white, semithick, minimum width=0.5cm, minimum height=0.5cm, font=\footnotesize, text height=0.2cm, drop shadow=ashadow }, event/.style={ draw=black, semithick, minimum width=0.4cm, minimum height=0.4cm, font=\scriptsize }, trap/.style={ trapezium, trapezium angle=67.5, draw, inner ysep=5pt, outer sep=0pt, minimum height=1.81mm, minimum width=0pt }, static-process/.style={ draw=black, fill=white, semithick, minimum width=0.5cm, minimum height=0.5cm, font=\footnotesize, text height=0.2cm }, pill/.style={ draw, % semithick, text=black, fill=white, minimum width=0.84em, minimum height=0.8em, inner sep=0.1em, outer sep=0, font=\scriptsize\sffamily, align=center, rounded corners=0.4em } } \pgfdeclaredecoration{penciline}{initial}{ \state{initial}[width=+\pgfdecoratedinputsegmentremainingdistance,auto corner on length=1mm,]{ \pgfpathcurveto% {% From \pgfqpoint{\pgfdecoratedinputsegmentremainingdistance}{\pgfdecorationsegmentamplitude} } {% Control 1 \pgfmathrand \pgfpointadd{\pgfqpoint{\pgfdecoratedinputsegmentremainingdistance}{0pt}}{\pgfqpoint{-\pgfdecorationsegmentaspect\pgfdecoratedinputsegmentremainingdistance}% {\pgfmathresult\pgfdecorationsegmentamplitude} } } {%TO \pgfpointadd{\pgfpointdecoratedinputsegmentlast}{\pgfpoint{1pt}{1pt}} } } \state{final}{} } \begin{document} \begin{tikzpicture} \node(monitor) [static-process]{\texttt{Monitor}}; \node(cm_c) [draw, left=0.2cm of monitor, font=\scriptsize] {$\textsf{CM}_c$}; \node(cm_m) [draw, right=0.2cm of monitor, font=\scriptsize] {$\textsf{CM}_s$}; \draw [thin, dotted, rounded corners] ($(cm_c.north west)+(-0.1cm,0.17cm)$) rectangle ($(cm_m.south east)+(0.1cm,-0.15cm)$); \node(server) [process, fill=gray!20, right=1.3cm of monitor] {$s$}; \node(client) [process, fill=gray!20, left=1.3cm of monitor] {$c$}; \node(cpspc) [draw, above=0.5cm of monitor, static-process, font=\footnotesize] {$\textsf{CPSPc}$}; \end{tikzpicture} \end{document}
example_30004_combination_2
\documentclass[12pt, a4paper]{elsarticle} \usepackage{amssymb} \usepackage{tikz} \usepackage{amsmath} \usepackage{xcolor} \usepackage{pgf} \usetikzlibrary{ matrix, shapes, arrows, shadows, calc, chains, decorations.pathmorphing, decorations.text, arrows.meta, patterns, fit, bending, shadows, shapes.geometric, snakes } \tikzset{ label/.style={ font=\scriptsize\itshape, inner sep=0.4em }, point/.style={ circle, fill=black, text width=0.3em, inner sep=0 }, state/.style={ circle, text width=0.8em, inner sep=0.1em, text depth=0.08em, draw, font=\scriptsize }, participant/.style={ draw=black, rounded corners, semithick, font=\footnotesize, text height=0.2cm, % minimum height=0.5cm, text centered, anchor=base }, specification/.style={ font=\small, semithick, draw=black }, synthesiser/.style={ draw=black, dotted, semithick, inner sep=2pt, font=\footnotesize }, monitor/.style={ % rounded corners=1mm, draw=black, fill=white, semithick, minimum width=0.5cm, minimum height=0.5cm, font=\footnotesize, text height=0.2cm, drop shadow=ashadow }, point/.style={ minimum size=0pt, inner sep=0pt }, ltspoint/.style={ circle, fill=black, draw=white, line width=0.5mm, text width=0.25em, inner sep=0, font=\footnotesize }, ashadow/.style={ opacity=.3, shadow xshift=0.6mm, shadow yshift=-0.6mm }, oppashadow/.style={ opacity=.3, shadow xshift=-0.6mm, shadow yshift=-0.6mm }, process/.style={ draw=black, fill=white, semithick, minimum width=0.5cm, minimum height=0.5cm, font=\footnotesize, text height=0.2cm, drop shadow=ashadow }, event/.style={ draw=black, semithick, minimum width=0.4cm, minimum height=0.4cm, font=\scriptsize }, trap/.style={ trapezium, trapezium angle=67.5, draw, inner ysep=5pt, outer sep=0pt, minimum height=1.81mm, minimum width=0pt }, static-process/.style={ draw=black, fill=white, semithick, minimum width=0.5cm, minimum height=0.5cm, font=\footnotesize, text height=0.2cm }, pill/.style={ draw, % semithick, text=black, fill=white, minimum width=0.84em, minimum height=0.8em, inner sep=0.1em, outer sep=0, font=\scriptsize\sffamily, align=center, rounded corners=0.4em } } \pgfdeclaredecoration{penciline}{initial}{ \state{initial}[width=+\pgfdecoratedinputsegmentremainingdistance,auto corner on length=1mm,]{ \pgfpathcurveto% {% From \pgfqpoint{\pgfdecoratedinputsegmentremainingdistance}{\pgfdecorationsegmentamplitude} } {% Control 1 \pgfmathrand \pgfpointadd{\pgfqpoint{\pgfdecoratedinputsegmentremainingdistance}{0pt}}{\pgfqpoint{-\pgfdecorationsegmentaspect\pgfdecoratedinputsegmentremainingdistance}% {\pgfmathresult\pgfdecorationsegmentamplitude} } } {%TO \pgfpointadd{\pgfpointdecoratedinputsegmentlast}{\pgfpoint{1pt}{1pt}} } } \state{final}{} } \begin{document} \begin{tikzpicture} \node(monitor) [static-process]{\texttt{Monitor}}; \node(cm_c) [draw, left=0.2cm of monitor, font=\scriptsize] {$\textsf{CM}_c$}; \node(cm_m) [draw, right=0.2cm of monitor, font=\scriptsize] {$\textsf{CM}_s$}; \end{tikzpicture} \end{document}
example_30004_combination_3
\documentclass[12pt, a4paper]{elsarticle} \usepackage{amssymb} \usepackage{tikz} \usepackage{amsmath} \usepackage{xcolor} \usepackage{pgf} \usetikzlibrary{ matrix, shapes, arrows, shadows, calc, chains, decorations.pathmorphing, decorations.text, arrows.meta, patterns, fit, bending, shadows, shapes.geometric, snakes } \tikzset{ label/.style={ font=\scriptsize\itshape, inner sep=0.4em }, point/.style={ circle, fill=black, text width=0.3em, inner sep=0 }, state/.style={ circle, text width=0.8em, inner sep=0.1em, text depth=0.08em, draw, font=\scriptsize }, participant/.style={ draw=black, rounded corners, semithick, font=\footnotesize, text height=0.2cm, % minimum height=0.5cm, text centered, anchor=base }, specification/.style={ font=\small, semithick, draw=black }, synthesiser/.style={ draw=black, dotted, semithick, inner sep=2pt, font=\footnotesize }, monitor/.style={ % rounded corners=1mm, draw=black, fill=white, semithick, minimum width=0.5cm, minimum height=0.5cm, font=\footnotesize, text height=0.2cm, drop shadow=ashadow }, point/.style={ minimum size=0pt, inner sep=0pt }, ltspoint/.style={ circle, fill=black, draw=white, line width=0.5mm, text width=0.25em, inner sep=0, font=\footnotesize }, ashadow/.style={ opacity=.3, shadow xshift=0.6mm, shadow yshift=-0.6mm }, oppashadow/.style={ opacity=.3, shadow xshift=-0.6mm, shadow yshift=-0.6mm }, process/.style={ draw=black, fill=white, semithick, minimum width=0.5cm, minimum height=0.5cm, font=\footnotesize, text height=0.2cm, drop shadow=ashadow }, event/.style={ draw=black, semithick, minimum width=0.4cm, minimum height=0.4cm, font=\scriptsize }, trap/.style={ trapezium, trapezium angle=67.5, draw, inner ysep=5pt, outer sep=0pt, minimum height=1.81mm, minimum width=0pt }, static-process/.style={ draw=black, fill=white, semithick, minimum width=0.5cm, minimum height=0.5cm, font=\footnotesize, text height=0.2cm }, pill/.style={ draw, % semithick, text=black, fill=white, minimum width=0.84em, minimum height=0.8em, inner sep=0.1em, outer sep=0, font=\scriptsize\sffamily, align=center, rounded corners=0.4em } } \pgfdeclaredecoration{penciline}{initial}{ \state{initial}[width=+\pgfdecoratedinputsegmentremainingdistance,auto corner on length=1mm,]{ \pgfpathcurveto% {% From \pgfqpoint{\pgfdecoratedinputsegmentremainingdistance}{\pgfdecorationsegmentamplitude} } {% Control 1 \pgfmathrand \pgfpointadd{\pgfqpoint{\pgfdecoratedinputsegmentremainingdistance}{0pt}}{\pgfqpoint{-\pgfdecorationsegmentaspect\pgfdecoratedinputsegmentremainingdistance}% {\pgfmathresult\pgfdecorationsegmentamplitude} } } {%TO \pgfpointadd{\pgfpointdecoratedinputsegmentlast}{\pgfpoint{1pt}{1pt}} } } \state{final}{} } \begin{document} \begin{tikzpicture} \node(monitor) [static-process]{\texttt{Monitor}}; \node(cm_c) [draw, left=0.2cm of monitor, font=\scriptsize] {$\textsf{CM}_c$}; \node(cm_m) [draw, right=0.2cm of monitor, font=\scriptsize] {$\textsf{CM}_s$}; \draw [thin, dotted, rounded corners] ($(cm_c.north west)+(-0.1cm,0.17cm)$) rectangle ($(cm_m.south east)+(0.1cm,-0.15cm)$); \end{tikzpicture} \end{document}
example_30004_combination_4
\documentclass[12pt, a4paper]{elsarticle} \usepackage{amssymb} \usepackage{tikz} \usepackage{amsmath} \usepackage{xcolor} \usepackage{pgf} \usetikzlibrary{ matrix, shapes, arrows, shadows, calc, chains, decorations.pathmorphing, decorations.text, arrows.meta, patterns, fit, bending, shadows, shapes.geometric, snakes } \tikzset{ label/.style={ font=\scriptsize\itshape, inner sep=0.4em }, point/.style={ circle, fill=black, text width=0.3em, inner sep=0 }, state/.style={ circle, text width=0.8em, inner sep=0.1em, text depth=0.08em, draw, font=\scriptsize }, participant/.style={ draw=black, rounded corners, semithick, font=\footnotesize, text height=0.2cm, % minimum height=0.5cm, text centered, anchor=base }, specification/.style={ font=\small, semithick, draw=black }, synthesiser/.style={ draw=black, dotted, semithick, inner sep=2pt, font=\footnotesize }, monitor/.style={ % rounded corners=1mm, draw=black, fill=white, semithick, minimum width=0.5cm, minimum height=0.5cm, font=\footnotesize, text height=0.2cm, drop shadow=ashadow }, point/.style={ minimum size=0pt, inner sep=0pt }, ltspoint/.style={ circle, fill=black, draw=white, line width=0.5mm, text width=0.25em, inner sep=0, font=\footnotesize }, ashadow/.style={ opacity=.3, shadow xshift=0.6mm, shadow yshift=-0.6mm }, oppashadow/.style={ opacity=.3, shadow xshift=-0.6mm, shadow yshift=-0.6mm }, process/.style={ draw=black, fill=white, semithick, minimum width=0.5cm, minimum height=0.5cm, font=\footnotesize, text height=0.2cm, drop shadow=ashadow }, event/.style={ draw=black, semithick, minimum width=0.4cm, minimum height=0.4cm, font=\scriptsize }, trap/.style={ trapezium, trapezium angle=67.5, draw, inner ysep=5pt, outer sep=0pt, minimum height=1.81mm, minimum width=0pt }, static-process/.style={ draw=black, fill=white, semithick, minimum width=0.5cm, minimum height=0.5cm, font=\footnotesize, text height=0.2cm }, pill/.style={ draw, % semithick, text=black, fill=white, minimum width=0.84em, minimum height=0.8em, inner sep=0.1em, outer sep=0, font=\scriptsize\sffamily, align=center, rounded corners=0.4em } } \pgfdeclaredecoration{penciline}{initial}{ \state{initial}[width=+\pgfdecoratedinputsegmentremainingdistance,auto corner on length=1mm,]{ \pgfpathcurveto% {% From \pgfqpoint{\pgfdecoratedinputsegmentremainingdistance}{\pgfdecorationsegmentamplitude} } {% Control 1 \pgfmathrand \pgfpointadd{\pgfqpoint{\pgfdecoratedinputsegmentremainingdistance}{0pt}}{\pgfqpoint{-\pgfdecorationsegmentaspect\pgfdecoratedinputsegmentremainingdistance}% {\pgfmathresult\pgfdecorationsegmentamplitude} } } {%TO \pgfpointadd{\pgfpointdecoratedinputsegmentlast}{\pgfpoint{1pt}{1pt}} } } \state{final}{} } \begin{document} \begin{tikzpicture} \node(monitor) [static-process]{\texttt{Monitor}}; \node(cm_c) [draw, left=0.2cm of monitor, font=\scriptsize] {$\textsf{CM}_c$}; \node(cm_m) [draw, right=0.2cm of monitor, font=\scriptsize] {$\textsf{CM}_s$}; \draw [thin, dotted, rounded corners] ($(cm_c.north west)+(-0.1cm,0.17cm)$) rectangle ($(cm_m.south east)+(0.1cm,-0.15cm)$); \node(server) [process, fill=gray!20, right=1.3cm of monitor] {$s$}; \end{tikzpicture} \end{document}
example_30004_combination_9
\documentclass[12pt, a4paper]{elsarticle} \usepackage{amssymb} \usepackage{tikz} \usepackage{amsmath} \usepackage{xcolor} \usepackage{pgf} \usetikzlibrary{ matrix, shapes, arrows, shadows, calc, chains, decorations.pathmorphing, decorations.text, arrows.meta, patterns, fit, bending, shadows, shapes.geometric, snakes } \tikzset{ label/.style={ font=\scriptsize\itshape, inner sep=0.4em }, point/.style={ circle, fill=black, text width=0.3em, inner sep=0 }, state/.style={ circle, text width=0.8em, inner sep=0.1em, text depth=0.08em, draw, font=\scriptsize }, participant/.style={ draw=black, rounded corners, semithick, font=\footnotesize, text height=0.2cm, % minimum height=0.5cm, text centered, anchor=base }, specification/.style={ font=\small, semithick, draw=black }, synthesiser/.style={ draw=black, dotted, semithick, inner sep=2pt, font=\footnotesize }, monitor/.style={ % rounded corners=1mm, draw=black, fill=white, semithick, minimum width=0.5cm, minimum height=0.5cm, font=\footnotesize, text height=0.2cm, drop shadow=ashadow }, point/.style={ minimum size=0pt, inner sep=0pt }, ltspoint/.style={ circle, fill=black, draw=white, line width=0.5mm, text width=0.25em, inner sep=0, font=\footnotesize }, ashadow/.style={ opacity=.3, shadow xshift=0.6mm, shadow yshift=-0.6mm }, oppashadow/.style={ opacity=.3, shadow xshift=-0.6mm, shadow yshift=-0.6mm }, process/.style={ draw=black, fill=white, semithick, minimum width=0.5cm, minimum height=0.5cm, font=\footnotesize, text height=0.2cm, drop shadow=ashadow }, event/.style={ draw=black, semithick, minimum width=0.4cm, minimum height=0.4cm, font=\scriptsize }, trap/.style={ trapezium, trapezium angle=67.5, draw, inner ysep=5pt, outer sep=0pt, minimum height=1.81mm, minimum width=0pt }, static-process/.style={ draw=black, fill=white, semithick, minimum width=0.5cm, minimum height=0.5cm, font=\footnotesize, text height=0.2cm }, pill/.style={ draw, % semithick, text=black, fill=white, minimum width=0.84em, minimum height=0.8em, inner sep=0.1em, outer sep=0, font=\scriptsize\sffamily, align=center, rounded corners=0.4em } } \pgfdeclaredecoration{penciline}{initial}{ \state{initial}[width=+\pgfdecoratedinputsegmentremainingdistance,auto corner on length=1mm,]{ \pgfpathcurveto% {% From \pgfqpoint{\pgfdecoratedinputsegmentremainingdistance}{\pgfdecorationsegmentamplitude} } {% Control 1 \pgfmathrand \pgfpointadd{\pgfqpoint{\pgfdecoratedinputsegmentremainingdistance}{0pt}}{\pgfqpoint{-\pgfdecorationsegmentaspect\pgfdecoratedinputsegmentremainingdistance}% {\pgfmathresult\pgfdecorationsegmentamplitude} } } {%TO \pgfpointadd{\pgfpointdecoratedinputsegmentlast}{\pgfpoint{1pt}{1pt}} } } \state{final}{} } \begin{document} \begin{tikzpicture} \node(monitor) [static-process]{\texttt{Monitor}}; \node(cm_c) [draw, left=0.2cm of monitor, font=\scriptsize] {$\textsf{CM}_c$}; \node(cm_m) [draw, right=0.2cm of monitor, font=\scriptsize] {$\textsf{CM}_s$}; \draw [thin, dotted, rounded corners] ($(cm_c.north west)+(-0.1cm,0.17cm)$) rectangle ($(cm_m.south east)+(0.1cm,-0.15cm)$); \node(server) [process, fill=gray!20, right=1.3cm of monitor] {$s$}; \node(client) [process, fill=gray!20, left=1.3cm of monitor] {$c$}; \node(cpspc) [draw, above=0.5cm of monitor, static-process, font=\footnotesize] {$\textsf{CPSPc}$}; \draw[-] (cm_c) -- (monitor); \draw[-] (cm_m) -- (monitor); \draw[-] (cpspc) -- (monitor); \draw[-] (cpspc) -| (cm_c); \draw[-] (cpspc) -| (cm_m); \draw[thin,double distance=2pt, fill=white] (cm_c) -- (client); \end{tikzpicture} \end{document}
example_30004_combination_7
\documentclass[12pt, a4paper]{elsarticle} \usepackage{amssymb} \usepackage{tikz} \usepackage{amsmath} \usepackage{xcolor} \usepackage{pgf} \usetikzlibrary{ matrix, shapes, arrows, shadows, calc, chains, decorations.pathmorphing, decorations.text, arrows.meta, patterns, fit, bending, shadows, shapes.geometric, snakes } \tikzset{ label/.style={ font=\scriptsize\itshape, inner sep=0.4em }, point/.style={ circle, fill=black, text width=0.3em, inner sep=0 }, state/.style={ circle, text width=0.8em, inner sep=0.1em, text depth=0.08em, draw, font=\scriptsize }, participant/.style={ draw=black, rounded corners, semithick, font=\footnotesize, text height=0.2cm, % minimum height=0.5cm, text centered, anchor=base }, specification/.style={ font=\small, semithick, draw=black }, synthesiser/.style={ draw=black, dotted, semithick, inner sep=2pt, font=\footnotesize }, monitor/.style={ % rounded corners=1mm, draw=black, fill=white, semithick, minimum width=0.5cm, minimum height=0.5cm, font=\footnotesize, text height=0.2cm, drop shadow=ashadow }, point/.style={ minimum size=0pt, inner sep=0pt }, ltspoint/.style={ circle, fill=black, draw=white, line width=0.5mm, text width=0.25em, inner sep=0, font=\footnotesize }, ashadow/.style={ opacity=.3, shadow xshift=0.6mm, shadow yshift=-0.6mm }, oppashadow/.style={ opacity=.3, shadow xshift=-0.6mm, shadow yshift=-0.6mm }, process/.style={ draw=black, fill=white, semithick, minimum width=0.5cm, minimum height=0.5cm, font=\footnotesize, text height=0.2cm, drop shadow=ashadow }, event/.style={ draw=black, semithick, minimum width=0.4cm, minimum height=0.4cm, font=\scriptsize }, trap/.style={ trapezium, trapezium angle=67.5, draw, inner ysep=5pt, outer sep=0pt, minimum height=1.81mm, minimum width=0pt }, static-process/.style={ draw=black, fill=white, semithick, minimum width=0.5cm, minimum height=0.5cm, font=\footnotesize, text height=0.2cm }, pill/.style={ draw, % semithick, text=black, fill=white, minimum width=0.84em, minimum height=0.8em, inner sep=0.1em, outer sep=0, font=\scriptsize\sffamily, align=center, rounded corners=0.4em } } \pgfdeclaredecoration{penciline}{initial}{ \state{initial}[width=+\pgfdecoratedinputsegmentremainingdistance,auto corner on length=1mm,]{ \pgfpathcurveto% {% From \pgfqpoint{\pgfdecoratedinputsegmentremainingdistance}{\pgfdecorationsegmentamplitude} } {% Control 1 \pgfmathrand \pgfpointadd{\pgfqpoint{\pgfdecoratedinputsegmentremainingdistance}{0pt}}{\pgfqpoint{-\pgfdecorationsegmentaspect\pgfdecoratedinputsegmentremainingdistance}% {\pgfmathresult\pgfdecorationsegmentamplitude} } } {%TO \pgfpointadd{\pgfpointdecoratedinputsegmentlast}{\pgfpoint{1pt}{1pt}} } } \state{final}{} } \begin{document} \begin{tikzpicture} \node(monitor) [static-process]{\texttt{Monitor}}; \node(cm_c) [draw, left=0.2cm of monitor, font=\scriptsize] {$\textsf{CM}_c$}; \node(cm_m) [draw, right=0.2cm of monitor, font=\scriptsize] {$\textsf{CM}_s$}; \draw [thin, dotted, rounded corners] ($(cm_c.north west)+(-0.1cm,0.17cm)$) rectangle ($(cm_m.south east)+(0.1cm,-0.15cm)$); \node(server) [process, fill=gray!20, right=1.3cm of monitor] {$s$}; \node(client) [process, fill=gray!20, left=1.3cm of monitor] {$c$}; \node(cpspc) [draw, above=0.5cm of monitor, static-process, font=\footnotesize] {$\textsf{CPSPc}$}; \draw[-] (cm_c) -- (monitor); \draw[-] (cm_m) -- (monitor); \end{tikzpicture} \end{document}
example_30004_combination_1
\documentclass[12pt, a4paper]{elsarticle} \usepackage{amssymb} \usepackage{tikz} \usepackage{amsmath} \usepackage{xcolor} \usepackage{pgf} \usetikzlibrary{ matrix, shapes, arrows, shadows, calc, chains, decorations.pathmorphing, decorations.text, arrows.meta, patterns, fit, bending, shadows, shapes.geometric, snakes } \tikzset{ label/.style={ font=\scriptsize\itshape, inner sep=0.4em }, point/.style={ circle, fill=black, text width=0.3em, inner sep=0 }, state/.style={ circle, text width=0.8em, inner sep=0.1em, text depth=0.08em, draw, font=\scriptsize }, participant/.style={ draw=black, rounded corners, semithick, font=\footnotesize, text height=0.2cm, % minimum height=0.5cm, text centered, anchor=base }, specification/.style={ font=\small, semithick, draw=black }, synthesiser/.style={ draw=black, dotted, semithick, inner sep=2pt, font=\footnotesize }, monitor/.style={ % rounded corners=1mm, draw=black, fill=white, semithick, minimum width=0.5cm, minimum height=0.5cm, font=\footnotesize, text height=0.2cm, drop shadow=ashadow }, point/.style={ minimum size=0pt, inner sep=0pt }, ltspoint/.style={ circle, fill=black, draw=white, line width=0.5mm, text width=0.25em, inner sep=0, font=\footnotesize }, ashadow/.style={ opacity=.3, shadow xshift=0.6mm, shadow yshift=-0.6mm }, oppashadow/.style={ opacity=.3, shadow xshift=-0.6mm, shadow yshift=-0.6mm }, process/.style={ draw=black, fill=white, semithick, minimum width=0.5cm, minimum height=0.5cm, font=\footnotesize, text height=0.2cm, drop shadow=ashadow }, event/.style={ draw=black, semithick, minimum width=0.4cm, minimum height=0.4cm, font=\scriptsize }, trap/.style={ trapezium, trapezium angle=67.5, draw, inner ysep=5pt, outer sep=0pt, minimum height=1.81mm, minimum width=0pt }, static-process/.style={ draw=black, fill=white, semithick, minimum width=0.5cm, minimum height=0.5cm, font=\footnotesize, text height=0.2cm }, pill/.style={ draw, % semithick, text=black, fill=white, minimum width=0.84em, minimum height=0.8em, inner sep=0.1em, outer sep=0, font=\scriptsize\sffamily, align=center, rounded corners=0.4em } } \pgfdeclaredecoration{penciline}{initial}{ \state{initial}[width=+\pgfdecoratedinputsegmentremainingdistance,auto corner on length=1mm,]{ \pgfpathcurveto% {% From \pgfqpoint{\pgfdecoratedinputsegmentremainingdistance}{\pgfdecorationsegmentamplitude} } {% Control 1 \pgfmathrand \pgfpointadd{\pgfqpoint{\pgfdecoratedinputsegmentremainingdistance}{0pt}}{\pgfqpoint{-\pgfdecorationsegmentaspect\pgfdecoratedinputsegmentremainingdistance}% {\pgfmathresult\pgfdecorationsegmentamplitude} } } {%TO \pgfpointadd{\pgfpointdecoratedinputsegmentlast}{\pgfpoint{1pt}{1pt}} } } \state{final}{} } \begin{document} \begin{tikzpicture} \node(monitor) [static-process]{\texttt{Monitor}}; \node(cm_c) [draw, left=0.2cm of monitor, font=\scriptsize] {$\textsf{CM}_c$}; \end{tikzpicture} \end{document}
example_30004_combination_6
\documentclass[12pt, a4paper]{elsarticle} \usepackage{amssymb} \usepackage{tikz} \usepackage{amsmath} \usepackage{xcolor} \usepackage{pgf} \usetikzlibrary{ matrix, shapes, arrows, shadows, calc, chains, decorations.pathmorphing, decorations.text, arrows.meta, patterns, fit, bending, shadows, shapes.geometric, snakes } \tikzset{ label/.style={ font=\scriptsize\itshape, inner sep=0.4em }, point/.style={ circle, fill=black, text width=0.3em, inner sep=0 }, state/.style={ circle, text width=0.8em, inner sep=0.1em, text depth=0.08em, draw, font=\scriptsize }, participant/.style={ draw=black, rounded corners, semithick, font=\footnotesize, text height=0.2cm, % minimum height=0.5cm, text centered, anchor=base }, specification/.style={ font=\small, semithick, draw=black }, synthesiser/.style={ draw=black, dotted, semithick, inner sep=2pt, font=\footnotesize }, monitor/.style={ % rounded corners=1mm, draw=black, fill=white, semithick, minimum width=0.5cm, minimum height=0.5cm, font=\footnotesize, text height=0.2cm, drop shadow=ashadow }, point/.style={ minimum size=0pt, inner sep=0pt }, ltspoint/.style={ circle, fill=black, draw=white, line width=0.5mm, text width=0.25em, inner sep=0, font=\footnotesize }, ashadow/.style={ opacity=.3, shadow xshift=0.6mm, shadow yshift=-0.6mm }, oppashadow/.style={ opacity=.3, shadow xshift=-0.6mm, shadow yshift=-0.6mm }, process/.style={ draw=black, fill=white, semithick, minimum width=0.5cm, minimum height=0.5cm, font=\footnotesize, text height=0.2cm, drop shadow=ashadow }, event/.style={ draw=black, semithick, minimum width=0.4cm, minimum height=0.4cm, font=\scriptsize }, trap/.style={ trapezium, trapezium angle=67.5, draw, inner ysep=5pt, outer sep=0pt, minimum height=1.81mm, minimum width=0pt }, static-process/.style={ draw=black, fill=white, semithick, minimum width=0.5cm, minimum height=0.5cm, font=\footnotesize, text height=0.2cm }, pill/.style={ draw, % semithick, text=black, fill=white, minimum width=0.84em, minimum height=0.8em, inner sep=0.1em, outer sep=0, font=\scriptsize\sffamily, align=center, rounded corners=0.4em } } \pgfdeclaredecoration{penciline}{initial}{ \state{initial}[width=+\pgfdecoratedinputsegmentremainingdistance,auto corner on length=1mm,]{ \pgfpathcurveto% {% From \pgfqpoint{\pgfdecoratedinputsegmentremainingdistance}{\pgfdecorationsegmentamplitude} } {% Control 1 \pgfmathrand \pgfpointadd{\pgfqpoint{\pgfdecoratedinputsegmentremainingdistance}{0pt}}{\pgfqpoint{-\pgfdecorationsegmentaspect\pgfdecoratedinputsegmentremainingdistance}% {\pgfmathresult\pgfdecorationsegmentamplitude} } } {%TO \pgfpointadd{\pgfpointdecoratedinputsegmentlast}{\pgfpoint{1pt}{1pt}} } } \state{final}{} } \begin{document} \begin{tikzpicture} \node(monitor) [static-process]{\texttt{Monitor}}; \node(cm_c) [draw, left=0.2cm of monitor, font=\scriptsize] {$\textsf{CM}_c$}; \node(cm_m) [draw, right=0.2cm of monitor, font=\scriptsize] {$\textsf{CM}_s$}; \draw [thin, dotted, rounded corners] ($(cm_c.north west)+(-0.1cm,0.17cm)$) rectangle ($(cm_m.south east)+(0.1cm,-0.15cm)$); \node(server) [process, fill=gray!20, right=1.3cm of monitor] {$s$}; \node(client) [process, fill=gray!20, left=1.3cm of monitor] {$c$}; \node(cpspc) [draw, above=0.5cm of monitor, static-process, font=\footnotesize] {$\textsf{CPSPc}$}; \draw[-] (cm_c) -- (monitor); \end{tikzpicture} \end{document}
example_30004_combination_8
\documentclass[12pt, a4paper]{elsarticle} \usepackage{amssymb} \usepackage{tikz} \usepackage{amsmath} \usepackage{xcolor} \usepackage{pgf} \usetikzlibrary{ matrix, shapes, arrows, shadows, calc, chains, decorations.pathmorphing, decorations.text, arrows.meta, patterns, fit, bending, shadows, shapes.geometric, snakes } \tikzset{ label/.style={ font=\scriptsize\itshape, inner sep=0.4em }, point/.style={ circle, fill=black, text width=0.3em, inner sep=0 }, state/.style={ circle, text width=0.8em, inner sep=0.1em, text depth=0.08em, draw, font=\scriptsize }, participant/.style={ draw=black, rounded corners, semithick, font=\footnotesize, text height=0.2cm, % minimum height=0.5cm, text centered, anchor=base }, specification/.style={ font=\small, semithick, draw=black }, synthesiser/.style={ draw=black, dotted, semithick, inner sep=2pt, font=\footnotesize }, monitor/.style={ % rounded corners=1mm, draw=black, fill=white, semithick, minimum width=0.5cm, minimum height=0.5cm, font=\footnotesize, text height=0.2cm, drop shadow=ashadow }, point/.style={ minimum size=0pt, inner sep=0pt }, ltspoint/.style={ circle, fill=black, draw=white, line width=0.5mm, text width=0.25em, inner sep=0, font=\footnotesize }, ashadow/.style={ opacity=.3, shadow xshift=0.6mm, shadow yshift=-0.6mm }, oppashadow/.style={ opacity=.3, shadow xshift=-0.6mm, shadow yshift=-0.6mm }, process/.style={ draw=black, fill=white, semithick, minimum width=0.5cm, minimum height=0.5cm, font=\footnotesize, text height=0.2cm, drop shadow=ashadow }, event/.style={ draw=black, semithick, minimum width=0.4cm, minimum height=0.4cm, font=\scriptsize }, trap/.style={ trapezium, trapezium angle=67.5, draw, inner ysep=5pt, outer sep=0pt, minimum height=1.81mm, minimum width=0pt }, static-process/.style={ draw=black, fill=white, semithick, minimum width=0.5cm, minimum height=0.5cm, font=\footnotesize, text height=0.2cm }, pill/.style={ draw, % semithick, text=black, fill=white, minimum width=0.84em, minimum height=0.8em, inner sep=0.1em, outer sep=0, font=\scriptsize\sffamily, align=center, rounded corners=0.4em } } \pgfdeclaredecoration{penciline}{initial}{ \state{initial}[width=+\pgfdecoratedinputsegmentremainingdistance,auto corner on length=1mm,]{ \pgfpathcurveto% {% From \pgfqpoint{\pgfdecoratedinputsegmentremainingdistance}{\pgfdecorationsegmentamplitude} } {% Control 1 \pgfmathrand \pgfpointadd{\pgfqpoint{\pgfdecoratedinputsegmentremainingdistance}{0pt}}{\pgfqpoint{-\pgfdecorationsegmentaspect\pgfdecoratedinputsegmentremainingdistance}% {\pgfmathresult\pgfdecorationsegmentamplitude} } } {%TO \pgfpointadd{\pgfpointdecoratedinputsegmentlast}{\pgfpoint{1pt}{1pt}} } } \state{final}{} } \begin{document} \begin{tikzpicture} \node(monitor) [static-process]{\texttt{Monitor}}; \node(cm_c) [draw, left=0.2cm of monitor, font=\scriptsize] {$\textsf{CM}_c$}; \node(cm_m) [draw, right=0.2cm of monitor, font=\scriptsize] {$\textsf{CM}_s$}; \draw [thin, dotted, rounded corners] ($(cm_c.north west)+(-0.1cm,0.17cm)$) rectangle ($(cm_m.south east)+(0.1cm,-0.15cm)$); \node(server) [process, fill=gray!20, right=1.3cm of monitor] {$s$}; \node(client) [process, fill=gray!20, left=1.3cm of monitor] {$c$}; \node(cpspc) [draw, above=0.5cm of monitor, static-process, font=\footnotesize] {$\textsf{CPSPc}$}; \draw[-] (cm_c) -- (monitor); \draw[-] (cm_m) -- (monitor); \draw[-] (cpspc) -- (monitor); \draw[-] (cpspc) -| (cm_c); \draw[-] (cpspc) -| (cm_m); \end{tikzpicture} \end{document}
example_30004_combination_10
\documentclass[12pt, a4paper]{elsarticle} \usepackage{amssymb} \usepackage{tikz} \usepackage{amsmath} \usepackage{xcolor} \usepackage{pgf} \usetikzlibrary{ matrix, shapes, arrows, shadows, calc, chains, decorations.pathmorphing, decorations.text, arrows.meta, patterns, fit, bending, shadows, shapes.geometric, snakes } \tikzset{ label/.style={ font=\scriptsize\itshape, inner sep=0.4em }, point/.style={ circle, fill=black, text width=0.3em, inner sep=0 }, state/.style={ circle, text width=0.8em, inner sep=0.1em, text depth=0.08em, draw, font=\scriptsize }, participant/.style={ draw=black, rounded corners, semithick, font=\footnotesize, text height=0.2cm, % minimum height=0.5cm, text centered, anchor=base }, specification/.style={ font=\small, semithick, draw=black }, synthesiser/.style={ draw=black, dotted, semithick, inner sep=2pt, font=\footnotesize }, monitor/.style={ % rounded corners=1mm, draw=black, fill=white, semithick, minimum width=0.5cm, minimum height=0.5cm, font=\footnotesize, text height=0.2cm, drop shadow=ashadow }, point/.style={ minimum size=0pt, inner sep=0pt }, ltspoint/.style={ circle, fill=black, draw=white, line width=0.5mm, text width=0.25em, inner sep=0, font=\footnotesize }, ashadow/.style={ opacity=.3, shadow xshift=0.6mm, shadow yshift=-0.6mm }, oppashadow/.style={ opacity=.3, shadow xshift=-0.6mm, shadow yshift=-0.6mm }, process/.style={ draw=black, fill=white, semithick, minimum width=0.5cm, minimum height=0.5cm, font=\footnotesize, text height=0.2cm, drop shadow=ashadow }, event/.style={ draw=black, semithick, minimum width=0.4cm, minimum height=0.4cm, font=\scriptsize }, trap/.style={ trapezium, trapezium angle=67.5, draw, inner ysep=5pt, outer sep=0pt, minimum height=1.81mm, minimum width=0pt }, static-process/.style={ draw=black, fill=white, semithick, minimum width=0.5cm, minimum height=0.5cm, font=\footnotesize, text height=0.2cm }, pill/.style={ draw, % semithick, text=black, fill=white, minimum width=0.84em, minimum height=0.8em, inner sep=0.1em, outer sep=0, font=\scriptsize\sffamily, align=center, rounded corners=0.4em } } \pgfdeclaredecoration{penciline}{initial}{ \state{initial}[width=+\pgfdecoratedinputsegmentremainingdistance,auto corner on length=1mm,]{ \pgfpathcurveto% {% From \pgfqpoint{\pgfdecoratedinputsegmentremainingdistance}{\pgfdecorationsegmentamplitude} } {% Control 1 \pgfmathrand \pgfpointadd{\pgfqpoint{\pgfdecoratedinputsegmentremainingdistance}{0pt}}{\pgfqpoint{-\pgfdecorationsegmentaspect\pgfdecoratedinputsegmentremainingdistance}% {\pgfmathresult\pgfdecorationsegmentamplitude} } } {%TO \pgfpointadd{\pgfpointdecoratedinputsegmentlast}{\pgfpoint{1pt}{1pt}} } } \state{final}{} } \begin{document} \begin{tikzpicture} \node(monitor) [static-process]{\texttt{Monitor}}; \node(cm_c) [draw, left=0.2cm of monitor, font=\scriptsize] {$\textsf{CM}_c$}; \node(cm_m) [draw, right=0.2cm of monitor, font=\scriptsize] {$\textsf{CM}_s$}; \draw [thin, dotted, rounded corners] ($(cm_c.north west)+(-0.1cm,0.17cm)$) rectangle ($(cm_m.south east)+(0.1cm,-0.15cm)$); \node(server) [process, fill=gray!20, right=1.3cm of monitor] {$s$}; \node(client) [process, fill=gray!20, left=1.3cm of monitor] {$c$}; \node(cpspc) [draw, above=0.5cm of monitor, static-process, font=\footnotesize] {$\textsf{CPSPc}$}; \draw[-] (cm_c) -- (monitor); \draw[-] (cm_m) -- (monitor); \draw[-] (cpspc) -- (monitor); \draw[-] (cpspc) -| (cm_c); \draw[-] (cpspc) -| (cm_m); \draw[thin,double distance=2pt, fill=white] (cm_c) -- (client); \draw[thin,double distance=2pt, fill=white] (cm_m) -- (server); \node(vm) [below=0.8mm of cm_c, font=\tiny, draw=white, fill=white, inner sep=0pt] {\texttt{VM}}; \end{tikzpicture} \end{document}
example_30004_main
\documentclass[12pt, a4paper]{elsarticle} \usepackage{amssymb} \usepackage{tikz} \usepackage{amsmath} \usepackage{xcolor} \usepackage{pgf} \usetikzlibrary{ matrix, shapes, arrows, shadows, calc, chains, decorations.pathmorphing, decorations.text, arrows.meta, patterns, fit, bending, shadows, shapes.geometric, snakes } \tikzset{ label/.style={ font=\scriptsize\itshape, inner sep=0.4em }, point/.style={ circle, fill=black, text width=0.3em, inner sep=0 }, state/.style={ circle, text width=0.8em, inner sep=0.1em, text depth=0.08em, draw, font=\scriptsize }, participant/.style={ draw=black, rounded corners, semithick, font=\footnotesize, text height=0.2cm, % minimum height=0.5cm, text centered, anchor=base }, specification/.style={ font=\small, semithick, draw=black }, synthesiser/.style={ draw=black, dotted, semithick, inner sep=2pt, font=\footnotesize }, monitor/.style={ % rounded corners=1mm, draw=black, fill=white, semithick, minimum width=0.5cm, minimum height=0.5cm, font=\footnotesize, text height=0.2cm, drop shadow=ashadow }, point/.style={ minimum size=0pt, inner sep=0pt }, ltspoint/.style={ circle, fill=black, draw=white, line width=0.5mm, text width=0.25em, inner sep=0, font=\footnotesize }, ashadow/.style={ opacity=.3, shadow xshift=0.6mm, shadow yshift=-0.6mm }, oppashadow/.style={ opacity=.3, shadow xshift=-0.6mm, shadow yshift=-0.6mm }, process/.style={ draw=black, fill=white, semithick, minimum width=0.5cm, minimum height=0.5cm, font=\footnotesize, text height=0.2cm, drop shadow=ashadow }, event/.style={ draw=black, semithick, minimum width=0.4cm, minimum height=0.4cm, font=\scriptsize }, trap/.style={ trapezium, trapezium angle=67.5, draw, inner ysep=5pt, outer sep=0pt, minimum height=1.81mm, minimum width=0pt }, static-process/.style={ draw=black, fill=white, semithick, minimum width=0.5cm, minimum height=0.5cm, font=\footnotesize, text height=0.2cm }, pill/.style={ draw, % semithick, text=black, fill=white, minimum width=0.84em, minimum height=0.8em, inner sep=0.1em, outer sep=0, font=\scriptsize\sffamily, align=center, rounded corners=0.4em } } \pgfdeclaredecoration{penciline}{initial}{ \state{initial}[width=+\pgfdecoratedinputsegmentremainingdistance,auto corner on length=1mm,]{ \pgfpathcurveto% {% From \pgfqpoint{\pgfdecoratedinputsegmentremainingdistance}{\pgfdecorationsegmentamplitude} } {% Control 1 \pgfmathrand \pgfpointadd{\pgfqpoint{\pgfdecoratedinputsegmentremainingdistance}{0pt}}{\pgfqpoint{-\pgfdecorationsegmentaspect\pgfdecoratedinputsegmentremainingdistance}% {\pgfmathresult\pgfdecorationsegmentamplitude} } } {%TO \pgfpointadd{\pgfpointdecoratedinputsegmentlast}{\pgfpoint{1pt}{1pt}} } } \state{final}{} } \begin{document} \begin{tikzpicture} \node(monitor) [static-process]{\texttt{Monitor}}; \node(cm_c) [draw, left=0.2cm of monitor, font=\scriptsize] {$\textsf{CM}_c$}; \node(cm_m) [draw, right=0.2cm of monitor, font=\scriptsize] {$\textsf{CM}_s$}; \draw [thin, dotted, rounded corners] ($(cm_c.north west)+(-0.1cm,0.17cm)$) rectangle ($(cm_m.south east)+(0.1cm,-0.15cm)$); \node(server) [process, fill=gray!20, right=1.3cm of monitor] {$s$}; \node(client) [process, fill=gray!20, left=1.3cm of monitor] {$c$}; \node(cpspc) [draw, above=0.5cm of monitor, static-process, font=\footnotesize] {$\textsf{CPSPc}$}; \draw[-] (cm_c) -- (monitor); \draw[-] (cm_m) -- (monitor); \draw[-] (cpspc) -- (monitor); \draw[-] (cpspc) -| (cm_c); \draw[-] (cpspc) -| (cm_m); \draw[thin,double distance=2pt, fill=white] (cm_c) -- (client); \draw[thin,double distance=2pt, fill=white] (cm_m) -- (server); \node(vm) [below=0.8mm of cm_c, font=\tiny, draw=white, fill=white, inner sep=0pt] {\texttt{VM}}; \end{tikzpicture} \end{document}
example_30005_combination_1
\documentclass[reqno]{amsart} \usepackage{amssymb} \usepackage{amsmath} \usepackage{tikz} \usepackage{color} \tikzset{vertex/.style={fill,circle,inner sep=1.0pt}} \begin{document} \begin{tikzpicture} \draw (0,0)--(0.5,1)--(-0.5,1)--cycle (0,0)--(0,-1); \end{tikzpicture} \end{document}
example_30005_combination_2
\documentclass[reqno]{amsart} \usepackage{amssymb} \usepackage{amsmath} \usepackage{tikz} \usepackage{color} \tikzset{vertex/.style={fill,circle,inner sep=1.0pt}} \begin{document} \begin{tikzpicture} \draw (0,0)--(0.5,1)--(-0.5,1)--cycle (0,0)--(0,-1); \foreach \x in {(0,0), (0.5,1), (-0.5,1), (0,-1)} {\node at \x [vertex] {};}; \node at (0,0) [left] {$v$}; \node at (0,-1) [left] {$w$}; \node at (0,-1.5) {$G$}; \end{tikzpicture} \end{document}
example_30005_main
\documentclass[reqno]{amsart} \usepackage{amssymb} \usepackage{amsmath} \usepackage{tikz} \usepackage{color} \tikzset{vertex/.style={fill,circle,inner sep=1.0pt}} \begin{document} \begin{tikzpicture} \draw (0,0)--(0.5,1)--(-0.5,1)--cycle (0,0)--(0,-1); \foreach \x in {(0,0), (0.5,1), (-0.5,1), (0,-1)} {\node at \x [vertex] {};}; \node at (0,0) [left] {$v$}; \node at (0,-1) [left] {$w$}; \node at (0,-1.5) {$G$}; \end{tikzpicture} \end{document}
example_30006_combination_3
\documentclass[reqno]{amsart} \usepackage{amssymb} \usepackage{amsmath} \usepackage{tikz} \usepackage{color} \tikzset{vertex/.style={fill,circle,inner sep=1.0pt}} \newcommand{\lex}[2]{{#1}[{#2}]} \begin{document} \begin{tikzpicture} \draw (1,1) grid (4,3); \draw (1,1)--(3,3) (1,2)--(2,3) (2,1)--(4,3) (3,1)--(4,2) (1,3)--(3,1) (1,2)--(2,1) (2,3)--(4,1) (3,3)--(4,2); \draw (1,1)--(3,2) (1,1)--(4,2) (2,1)--(4,2) (3,1)--(1,2) (4,1)--(1,2) (4,1)--(2,2) (1,2)--(3,3) (1,2)--(4,3) (2,2)--(4,3) (3,2)--(1,3) (4,2)--(1,3) (4,2)--(2,3); \end{tikzpicture} \end{document}
example_30006_combination_4
\documentclass[reqno]{amsart} \usepackage{amssymb} \usepackage{amsmath} \usepackage{tikz} \usepackage{color} \tikzset{vertex/.style={fill,circle,inner sep=1.0pt}} \newcommand{\lex}[2]{{#1}[{#2}]} \begin{document} \begin{tikzpicture} \draw (1,1) grid (4,3); \draw (1,1)--(3,3) (1,2)--(2,3) (2,1)--(4,3) (3,1)--(4,2) (1,3)--(3,1) (1,2)--(2,1) (2,3)--(4,1) (3,3)--(4,2); \draw (1,1)--(3,2) (1,1)--(4,2) (2,1)--(4,2) (3,1)--(1,2) (4,1)--(1,2) (4,1)--(2,2) (1,2)--(3,3) (1,2)--(4,3) (2,2)--(4,3) (3,2)--(1,3) (4,2)--(1,3) (4,2)--(2,3); \foreach \x in {1,2,3,4} {\foreach \y in {1,2,3 } {\node at (\x, \y) [vertex] {};};} \node at (2.5,0.5) {$\lex{L_3}{L_4}$}; \end{tikzpicture} \end{document}
example_30006_combination_2
\documentclass[reqno]{amsart} \usepackage{amssymb} \usepackage{amsmath} \usepackage{tikz} \usepackage{color} \tikzset{vertex/.style={fill,circle,inner sep=1.0pt}} \newcommand{\lex}[2]{{#1}[{#2}]} \begin{document} \begin{tikzpicture} \draw (1,1) grid (4,3); \draw (1,1)--(3,3) (1,2)--(2,3) (2,1)--(4,3) (3,1)--(4,2) (1,3)--(3,1) (1,2)--(2,1) (2,3)--(4,1) (3,3)--(4,2); \end{tikzpicture} \end{document}
example_30006_combination_1
\documentclass[reqno]{amsart} \usepackage{amssymb} \usepackage{amsmath} \usepackage{tikz} \usepackage{color} \tikzset{vertex/.style={fill,circle,inner sep=1.0pt}} \newcommand{\lex}[2]{{#1}[{#2}]} \begin{document} \begin{tikzpicture} \draw (1,1) grid (4,3); \end{tikzpicture} \end{document}
example_30006_main
\documentclass[reqno]{amsart} \usepackage{amssymb} \usepackage{amsmath} \usepackage{tikz} \usepackage{color} \tikzset{vertex/.style={fill,circle,inner sep=1.0pt}} \newcommand{\lex}[2]{{#1}[{#2}]} \begin{document} \begin{tikzpicture} \draw (1,1) grid (4,3); \draw (1,1)--(3,3) (1,2)--(2,3) (2,1)--(4,3) (3,1)--(4,2) (1,3)--(3,1) (1,2)--(2,1) (2,3)--(4,1) (3,3)--(4,2); \draw (1,1)--(3,2) (1,1)--(4,2) (2,1)--(4,2) (3,1)--(1,2) (4,1)--(1,2) (4,1)--(2,2) (1,2)--(3,3) (1,2)--(4,3) (2,2)--(4,3) (3,2)--(1,3) (4,2)--(1,3) (4,2)--(2,3); \foreach \x in {1,2,3,4} {\foreach \y in {1,2,3 } {\node at (\x, \y) [vertex] {};};} \node at (2.5,0.5) {$\lex{L_3}{L_4}$}; \end{tikzpicture} \end{document}
example_30007_combination_2
\documentclass[reqno]{amsart} \usepackage{amssymb} \usepackage{amsmath} \usepackage{tikz} \usepackage{color} \tikzset{vertex/.style={fill,circle,inner sep=1.0pt}} \newcommand{\lex}[2]{{#1}[{#2}]} \begin{document} \begin{tikzpicture} \draw (1,1) grid (4,3); \draw (1,1)--(3,3) (1,2)--(2,3) (2,1)--(4,3) (3,1)--(4,2) (1,3)--(3,1) (1,2)--(2,1) (2,3)--(4,1) (3,3)--(4,2); \end{tikzpicture} \end{document}
example_30007_combination_4
\documentclass[reqno]{amsart} \usepackage{amssymb} \usepackage{amsmath} \usepackage{tikz} \usepackage{color} \tikzset{vertex/.style={fill,circle,inner sep=1.0pt}} \newcommand{\lex}[2]{{#1}[{#2}]} \begin{document} \begin{tikzpicture} \draw (1,1) grid (4,3); \draw (1,1)--(3,3) (1,2)--(2,3) (2,1)--(4,3) (3,1)--(4,2) (1,3)--(3,1) (1,2)--(2,1) (2,3)--(4,1) (3,3)--(4,2); \draw (1,1)--(2,3) (1,3)--(2,1) (2,1)--(3,3) (2,3)--(3,1) (3,1)--(4,3) (3,3)--(4,1); \foreach \x in {1,2,3,4} {\foreach \y in {1,2,3 } {\node at (\x, \y) [vertex] {};};} \node at (2.5,0.5) {$\lex{L_4}{L_3}$}; \end{tikzpicture} \end{document}
example_30007_combination_3
\documentclass[reqno]{amsart} \usepackage{amssymb} \usepackage{amsmath} \usepackage{tikz} \usepackage{color} \tikzset{vertex/.style={fill,circle,inner sep=1.0pt}} \newcommand{\lex}[2]{{#1}[{#2}]} \begin{document} \begin{tikzpicture} \draw (1,1) grid (4,3); \draw (1,1)--(3,3) (1,2)--(2,3) (2,1)--(4,3) (3,1)--(4,2) (1,3)--(3,1) (1,2)--(2,1) (2,3)--(4,1) (3,3)--(4,2); \draw (1,1)--(2,3) (1,3)--(2,1) (2,1)--(3,3) (2,3)--(3,1) (3,1)--(4,3) (3,3)--(4,1); \end{tikzpicture} \end{document}
example_30007_combination_1
\documentclass[reqno]{amsart} \usepackage{amssymb} \usepackage{amsmath} \usepackage{tikz} \usepackage{color} \tikzset{vertex/.style={fill,circle,inner sep=1.0pt}} \newcommand{\lex}[2]{{#1}[{#2}]} \begin{document} \begin{tikzpicture} \draw (1,1) grid (4,3); \end{tikzpicture} \end{document}
example_30007_main
\documentclass[reqno]{amsart} \usepackage{amssymb} \usepackage{amsmath} \usepackage{tikz} \usepackage{color} \tikzset{vertex/.style={fill,circle,inner sep=1.0pt}} \newcommand{\lex}[2]{{#1}[{#2}]} \begin{document} \begin{tikzpicture} \draw (1,1) grid (4,3); \draw (1,1)--(3,3) (1,2)--(2,3) (2,1)--(4,3) (3,1)--(4,2) (1,3)--(3,1) (1,2)--(2,1) (2,3)--(4,1) (3,3)--(4,2); \draw (1,1)--(2,3) (1,3)--(2,1) (2,1)--(3,3) (2,3)--(3,1) (3,1)--(4,3) (3,3)--(4,1); \foreach \x in {1,2,3,4} {\foreach \y in {1,2,3 } {\node at (\x, \y) [vertex] {};};} \node at (2.5,0.5) {$\lex{L_4}{L_3}$}; \end{tikzpicture} \end{document}
example_30008_combination_1
\documentclass[reqno]{amsart} \usepackage{amssymb} \usepackage{amsmath} \usepackage{tikz} \usepackage{color} \tikzset{vertex/.style={fill,circle,inner sep=1.0pt}} \begin{document} \begin{tikzpicture} \draw (0.5,1)--(0,-1)--(-0.5,1); \end{tikzpicture} \end{document}
example_30008_combination_2
\documentclass[reqno]{amsart} \usepackage{amssymb} \usepackage{amsmath} \usepackage{tikz} \usepackage{color} \tikzset{vertex/.style={fill,circle,inner sep=1.0pt}} \begin{document} \begin{tikzpicture} \draw (0.5,1)--(0,-1)--(-0.5,1); \foreach \x in {(0,0), (0.5,1), (-0.5,1), (0,-1)} {\node at \x [vertex] {};}; \node at (0,0) [above] {$v$}; \node at (0,-1) [left] {$w$}; \node at (0,-1.5) {$I(G)$}; \end{tikzpicture} \end{document}
example_30008_main
\documentclass[reqno]{amsart} \usepackage{amssymb} \usepackage{amsmath} \usepackage{tikz} \usepackage{color} \tikzset{vertex/.style={fill,circle,inner sep=1.0pt}} \begin{document} \begin{tikzpicture} \draw (0.5,1)--(0,-1)--(-0.5,1); \foreach \x in {(0,0), (0.5,1), (-0.5,1), (0,-1)} {\node at \x [vertex] {};}; \node at (0,0) [above] {$v$}; \node at (0,-1) [left] {$w$}; \node at (0,-1.5) {$I(G)$}; \end{tikzpicture} \end{document}
example_30009_combination_6
\documentclass[reqno]{amsart} \usepackage{amssymb} \usepackage{amsmath} \usepackage{tikz} \usepackage{color} \tikzset{vertex/.style={fill,circle,inner sep=1.0pt}} \begin{document} \begin{tikzpicture} \node at (1,1) [vertex] {}; \node at (1,1) [left] {$a$}; \node at (1,2) [vertex] {}; \node at (1,2) [left] {$b$}; \node at (2,1) [vertex] {}; \node at (2,1) [right] {$c$}; \node at (2,2) [vertex] {}; \node at (2,2) [right] {$d$}; \draw (1,2)--(2,1)--(1,1)--(2,2); \node at (1.5, 0.5) {$(X_1 * A_2) \cup (A_1 * X_2)$}; \end{tikzpicture} \end{document}
example_30009_combination_1
\documentclass[reqno]{amsart} \usepackage{amssymb} \usepackage{amsmath} \usepackage{tikz} \usepackage{color} \tikzset{vertex/.style={fill,circle,inner sep=1.0pt}} \begin{document} \begin{tikzpicture} \node at (1,1) [vertex] {}; \node at (1,1) [left] {$a$}; \end{tikzpicture} \end{document}
example_30009_combination_4
\documentclass[reqno]{amsart} \usepackage{amssymb} \usepackage{amsmath} \usepackage{tikz} \usepackage{color} \tikzset{vertex/.style={fill,circle,inner sep=1.0pt}} \begin{document} \begin{tikzpicture} \node at (1,1) [vertex] {}; \node at (1,1) [left] {$a$}; \node at (1,2) [vertex] {}; \node at (1,2) [left] {$b$}; \node at (2,1) [vertex] {}; \node at (2,1) [right] {$c$}; \node at (2,2) [vertex] {}; \node at (2,2) [right] {$d$}; \end{tikzpicture} \end{document}
example_30009_combination_3
\documentclass[reqno]{amsart} \usepackage{amssymb} \usepackage{amsmath} \usepackage{tikz} \usepackage{color} \tikzset{vertex/.style={fill,circle,inner sep=1.0pt}} \begin{document} \begin{tikzpicture} \node at (1,1) [vertex] {}; \node at (1,1) [left] {$a$}; \node at (1,2) [vertex] {}; \node at (1,2) [left] {$b$}; \node at (2,1) [vertex] {}; \node at (2,1) [right] {$c$}; \end{tikzpicture} \end{document}
example_30009_combination_2
\documentclass[reqno]{amsart} \usepackage{amssymb} \usepackage{amsmath} \usepackage{tikz} \usepackage{color} \tikzset{vertex/.style={fill,circle,inner sep=1.0pt}} \begin{document} \begin{tikzpicture} \node at (1,1) [vertex] {}; \node at (1,1) [left] {$a$}; \node at (1,2) [vertex] {}; \node at (1,2) [left] {$b$}; \end{tikzpicture} \end{document}
example_30009_combination_5
\documentclass[reqno]{amsart} \usepackage{amssymb} \usepackage{amsmath} \usepackage{tikz} \usepackage{color} \tikzset{vertex/.style={fill,circle,inner sep=1.0pt}} \begin{document} \begin{tikzpicture} \node at (1,1) [vertex] {}; \node at (1,1) [left] {$a$}; \node at (1,2) [vertex] {}; \node at (1,2) [left] {$b$}; \node at (2,1) [vertex] {}; \node at (2,1) [right] {$c$}; \node at (2,2) [vertex] {}; \node at (2,2) [right] {$d$}; \draw (1,2)--(2,1)--(1,1)--(2,2); \end{tikzpicture} \end{document}
example_30009_main
\documentclass[reqno]{amsart} \usepackage{amssymb} \usepackage{amsmath} \usepackage{tikz} \usepackage{color} \tikzset{vertex/.style={fill,circle,inner sep=1.0pt}} \begin{document} \begin{tikzpicture} \node at (1,1) [vertex] {}; \node at (1,1) [left] {$a$}; \node at (1,2) [vertex] {}; \node at (1,2) [left] {$b$}; \node at (2,1) [vertex] {}; \node at (2,1) [right] {$c$}; \node at (2,2) [vertex] {}; \node at (2,2) [right] {$d$}; \draw (1,2)--(2,1)--(1,1)--(2,2); \node at (1.5, 0.5) {$(X_1 * A_2) \cup (A_1 * X_2)$}; \end{tikzpicture} \end{document}
example_30010_combination_1
\documentclass[reqno]{amsart} \usepackage{amssymb} \usepackage{amsmath} \usepackage{tikz} \usepackage{color} \tikzset{vertex/.style={fill,circle,inner sep=1.0pt}} \newcommand{\dl}[2]{\mathrm{dl}_{#1}(#2)} \begin{document} \begin{tikzpicture} \draw (0.5,1)--(0,-1)--(-0.5,1); \end{tikzpicture} \end{document}
example_30010_combination_2
\documentclass[reqno]{amsart} \usepackage{amssymb} \usepackage{amsmath} \usepackage{tikz} \usepackage{color} \tikzset{vertex/.style={fill,circle,inner sep=1.0pt}} \newcommand{\dl}[2]{\mathrm{dl}_{#1}(#2)} \begin{document} \begin{tikzpicture} \draw (0.5,1)--(0,-1)--(-0.5,1); \foreach \x in {(0.5,1), (-0.5,1), (0,-1)} {\node at \x [vertex] {};}; \node at (0,-1) [left] {$w$}; \node at (0,-1.5) {$\dl{I(G)}{v}$}; \end{tikzpicture} \end{document}
example_30010_main
\documentclass[reqno]{amsart} \usepackage{amssymb} \usepackage{amsmath} \usepackage{tikz} \usepackage{color} \tikzset{vertex/.style={fill,circle,inner sep=1.0pt}} \newcommand{\dl}[2]{\mathrm{dl}_{#1}(#2)} \begin{document} \begin{tikzpicture} \draw (0.5,1)--(0,-1)--(-0.5,1); \foreach \x in {(0.5,1), (-0.5,1), (0,-1)} {\node at \x [vertex] {};}; \node at (0,-1) [left] {$w$}; \node at (0,-1.5) {$\dl{I(G)}{v}$}; \end{tikzpicture} \end{document}
example_30011_combination_3
\documentclass[reqno]{amsart} \usepackage{amssymb} \usepackage{amsmath} \usepackage{tikz} \usepackage{color} \tikzset{vertex/.style={fill,circle,inner sep=1.0pt}} \begin{document} \begin{tikzpicture} \node at (-0.865, 1) [vertex] {}; \node at (-0.865,0) [vertex] {}; \node at (0,0.5) [vertex] {}; \node at (0,-0.5) [vertex] {}; \end{tikzpicture} \end{document}
example_30011_combination_4
\documentclass[reqno]{amsart} \usepackage{amssymb} \usepackage{amsmath} \usepackage{tikz} \usepackage{color} \tikzset{vertex/.style={fill,circle,inner sep=1.0pt}} \begin{document} \begin{tikzpicture} \node at (-0.865, 1) [vertex] {}; \node at (-0.865,0) [vertex] {}; \node at (0,0.5) [vertex] {}; \node at (0,-0.5) [vertex] {}; \node at (0.865, 1) [vertex] {}; \end{tikzpicture} \end{document}
example_30011_combination_10
\documentclass[reqno]{amsart} \usepackage{amssymb} \usepackage{amsmath} \usepackage{tikz} \usepackage{color} \tikzset{vertex/.style={fill,circle,inner sep=1.0pt}} \begin{document} \begin{tikzpicture} \node at (-0.865, 1) [vertex] {}; \node at (-0.865,0) [vertex] {}; \node at (0,0.5) [vertex] {}; \node at (0,-0.5) [vertex] {}; \node at (0.865, 1) [vertex] {}; \node at (0.865,0) [vertex] {}; \fill [opacity=0.3] (0,0.5)--(-0.865,1)--(-0.865,0)--(0,-0.5)--(0.865,0)--(0.865,1)--cycle; \draw (0,0.5)--(-0.865,1)--(-0.865,0)--(0,-0.5)--(0.865,0)--(0.865,1)--cycle (0,0.5)--(-0.865,0) (0,0.5)--(0,-0.5) (0, 0.5)--(0.865, 0); \node at (-0.865, 1) [left] {$a$}; \node at (-0.865,0) [left] {$b$}; \node at (0,0.5) [above] {$u$}; \node at (0,-0.5) [below] {$v$}; \node at (0.865, 1) [right] {$d$}; \node at (0.865,0) [right] {$c$}; \node at (0,-1) {$K$}; \end{tikzpicture} \end{document}
example_30011_combination_5
\documentclass[reqno]{amsart} \usepackage{amssymb} \usepackage{amsmath} \usepackage{tikz} \usepackage{color} \tikzset{vertex/.style={fill,circle,inner sep=1.0pt}} \begin{document} \begin{tikzpicture} \node at (-0.865, 1) [vertex] {}; \node at (-0.865,0) [vertex] {}; \node at (0,0.5) [vertex] {}; \node at (0,-0.5) [vertex] {}; \node at (0.865, 1) [vertex] {}; \node at (0.865,0) [vertex] {}; \end{tikzpicture} \end{document}
example_30011_combination_2
\documentclass[reqno]{amsart} \usepackage{amssymb} \usepackage{amsmath} \usepackage{tikz} \usepackage{color} \tikzset{vertex/.style={fill,circle,inner sep=1.0pt}} \begin{document} \begin{tikzpicture} \node at (-0.865, 1) [vertex] {}; \node at (-0.865,0) [vertex] {}; \node at (0,0.5) [vertex] {}; \end{tikzpicture} \end{document}
example_30011_combination_8
\documentclass[reqno]{amsart} \usepackage{amssymb} \usepackage{amsmath} \usepackage{tikz} \usepackage{color} \tikzset{vertex/.style={fill,circle,inner sep=1.0pt}} \begin{document} \begin{tikzpicture} \node at (-0.865, 1) [vertex] {}; \node at (-0.865,0) [vertex] {}; \node at (0,0.5) [vertex] {}; \node at (0,-0.5) [vertex] {}; \node at (0.865, 1) [vertex] {}; \node at (0.865,0) [vertex] {}; \fill [opacity=0.3] (0,0.5)--(-0.865,1)--(-0.865,0)--(0,-0.5)--(0.865,0)--(0.865,1)--cycle; \draw (0,0.5)--(-0.865,1)--(-0.865,0)--(0,-0.5)--(0.865,0)--(0.865,1)--cycle (0,0.5)--(-0.865,0) (0,0.5)--(0,-0.5) (0, 0.5)--(0.865, 0); \node at (-0.865, 1) [left] {$a$}; \node at (-0.865,0) [left] {$b$}; \node at (0,0.5) [above] {$u$}; \end{tikzpicture} \end{document}
example_30011_combination_1
\documentclass[reqno]{amsart} \usepackage{amssymb} \usepackage{amsmath} \usepackage{tikz} \usepackage{color} \tikzset{vertex/.style={fill,circle,inner sep=1.0pt}} \begin{document} \begin{tikzpicture} \node at (-0.865, 1) [vertex] {}; \end{tikzpicture} \end{document}
example_30011_combination_6
\documentclass[reqno]{amsart} \usepackage{amssymb} \usepackage{amsmath} \usepackage{tikz} \usepackage{color} \tikzset{vertex/.style={fill,circle,inner sep=1.0pt}} \begin{document} \begin{tikzpicture} \node at (-0.865, 1) [vertex] {}; \node at (-0.865,0) [vertex] {}; \node at (0,0.5) [vertex] {}; \node at (0,-0.5) [vertex] {}; \node at (0.865, 1) [vertex] {}; \node at (0.865,0) [vertex] {}; \fill [opacity=0.3] (0,0.5)--(-0.865,1)--(-0.865,0)--(0,-0.5)--(0.865,0)--(0.865,1)--cycle; \draw (0,0.5)--(-0.865,1)--(-0.865,0)--(0,-0.5)--(0.865,0)--(0.865,1)--cycle (0,0.5)--(-0.865,0) (0,0.5)--(0,-0.5) (0, 0.5)--(0.865, 0); \end{tikzpicture} \end{document}
example_30011_combination_7
\documentclass[reqno]{amsart} \usepackage{amssymb} \usepackage{amsmath} \usepackage{tikz} \usepackage{color} \tikzset{vertex/.style={fill,circle,inner sep=1.0pt}} \begin{document} \begin{tikzpicture} \node at (-0.865, 1) [vertex] {}; \node at (-0.865,0) [vertex] {}; \node at (0,0.5) [vertex] {}; \node at (0,-0.5) [vertex] {}; \node at (0.865, 1) [vertex] {}; \node at (0.865,0) [vertex] {}; \fill [opacity=0.3] (0,0.5)--(-0.865,1)--(-0.865,0)--(0,-0.5)--(0.865,0)--(0.865,1)--cycle; \draw (0,0.5)--(-0.865,1)--(-0.865,0)--(0,-0.5)--(0.865,0)--(0.865,1)--cycle (0,0.5)--(-0.865,0) (0,0.5)--(0,-0.5) (0, 0.5)--(0.865, 0); \node at (-0.865, 1) [left] {$a$}; \end{tikzpicture} \end{document}
example_30011_combination_9
\documentclass[reqno]{amsart} \usepackage{amssymb} \usepackage{amsmath} \usepackage{tikz} \usepackage{color} \tikzset{vertex/.style={fill,circle,inner sep=1.0pt}} \begin{document} \begin{tikzpicture} \node at (-0.865, 1) [vertex] {}; \node at (-0.865,0) [vertex] {}; \node at (0,0.5) [vertex] {}; \node at (0,-0.5) [vertex] {}; \node at (0.865, 1) [vertex] {}; \node at (0.865,0) [vertex] {}; \fill [opacity=0.3] (0,0.5)--(-0.865,1)--(-0.865,0)--(0,-0.5)--(0.865,0)--(0.865,1)--cycle; \draw (0,0.5)--(-0.865,1)--(-0.865,0)--(0,-0.5)--(0.865,0)--(0.865,1)--cycle (0,0.5)--(-0.865,0) (0,0.5)--(0,-0.5) (0, 0.5)--(0.865, 0); \node at (-0.865, 1) [left] {$a$}; \node at (-0.865,0) [left] {$b$}; \node at (0,0.5) [above] {$u$}; \node at (0,-0.5) [below] {$v$}; \node at (0.865, 1) [right] {$d$}; \end{tikzpicture} \end{document}
example_30011_main
\documentclass[reqno]{amsart} \usepackage{amssymb} \usepackage{amsmath} \usepackage{tikz} \usepackage{color} \tikzset{vertex/.style={fill,circle,inner sep=1.0pt}} \begin{document} \begin{tikzpicture} \node at (-0.865, 1) [vertex] {}; \node at (-0.865,0) [vertex] {}; \node at (0,0.5) [vertex] {}; \node at (0,-0.5) [vertex] {}; \node at (0.865, 1) [vertex] {}; \node at (0.865,0) [vertex] {}; \fill [opacity=0.3] (0,0.5)--(-0.865,1)--(-0.865,0)--(0,-0.5)--(0.865,0)--(0.865,1)--cycle; \draw (0,0.5)--(-0.865,1)--(-0.865,0)--(0,-0.5)--(0.865,0)--(0.865,1)--cycle (0,0.5)--(-0.865,0) (0,0.5)--(0,-0.5) (0, 0.5)--(0.865, 0); \node at (-0.865, 1) [left] {$a$}; \node at (-0.865,0) [left] {$b$}; \node at (0,0.5) [above] {$u$}; \node at (0,-0.5) [below] {$v$}; \node at (0.865, 1) [right] {$d$}; \node at (0.865,0) [right] {$c$}; \node at (0,-1) {$K$}; \end{tikzpicture} \end{document}
example_30012_combination_1
\documentclass[reqno]{amsart} \usepackage{amssymb} \usepackage{amsmath} \usepackage{tikz} \usepackage{color} \tikzset{vertex/.style={fill,circle,inner sep=1.0pt}} \newcommand{\lk}[2]{\mathrm{lk}_{#1}(#2)} \begin{document} \begin{tikzpicture} \node at (0,0) {$\emptyset$}; \end{tikzpicture} \end{document}
example_30012_combination_2
\documentclass[reqno]{amsart} \usepackage{amssymb} \usepackage{amsmath} \usepackage{tikz} \usepackage{color} \tikzset{vertex/.style={fill,circle,inner sep=1.0pt}} \newcommand{\lk}[2]{\mathrm{lk}_{#1}(#2)} \begin{document} \begin{tikzpicture} \node at (0,0) {$\emptyset$}; \node at (0,-1.5) {$\lk{I(G)}{v}$}; \end{tikzpicture} \end{document}
example_30012_main
\documentclass[reqno]{amsart} \usepackage{amssymb} \usepackage{amsmath} \usepackage{tikz} \usepackage{color} \tikzset{vertex/.style={fill,circle,inner sep=1.0pt}} \newcommand{\lk}[2]{\mathrm{lk}_{#1}(#2)} \begin{document} \begin{tikzpicture} \node at (0,0) {$\emptyset$}; \node at (0,-1.5) {$\lk{I(G)}{v}$}; \end{tikzpicture} \end{document}
example_30013_combination_4
\documentclass[reqno]{amsart} \usepackage{amssymb} \usepackage{amsmath} \usepackage{tikz} \usepackage{color} \tikzset{vertex/.style={fill,circle,inner sep=1.0pt}} \begin{document} \begin{tikzpicture} \node at (1,1) [vertex] {}; \node at (1,1) [left] {$a$}; \node at (1,2) [vertex] {}; \node at (1,2) [left] {$b$}; \node at (2,1) [vertex] {}; \node at (2,1) [right] {$c$}; \node at (2,2) [vertex] {}; \node at (2,2) [right] {$d$}; \end{tikzpicture} \end{document}
example_30013_combination_3
\documentclass[reqno]{amsart} \usepackage{amssymb} \usepackage{amsmath} \usepackage{tikz} \usepackage{color} \tikzset{vertex/.style={fill,circle,inner sep=1.0pt}} \begin{document} \begin{tikzpicture} \node at (1,1) [vertex] {}; \node at (1,1) [left] {$a$}; \node at (1,2) [vertex] {}; \node at (1,2) [left] {$b$}; \node at (2,1) [vertex] {}; \node at (2,1) [right] {$c$}; \end{tikzpicture} \end{document}
example_30013_combination_2
\documentclass[reqno]{amsart} \usepackage{amssymb} \usepackage{amsmath} \usepackage{tikz} \usepackage{color} \tikzset{vertex/.style={fill,circle,inner sep=1.0pt}} \begin{document} \begin{tikzpicture} \node at (1,1) [vertex] {}; \node at (1,1) [left] {$a$}; \node at (1,2) [vertex] {}; \node at (1,2) [left] {$b$}; \end{tikzpicture} \end{document}
example_30013_combination_5
\documentclass[reqno]{amsart} \usepackage{amssymb} \usepackage{amsmath} \usepackage{tikz} \usepackage{color} \tikzset{vertex/.style={fill,circle,inner sep=1.0pt}} \begin{document} \begin{tikzpicture} \node at (1,1) [vertex] {}; \node at (1,1) [left] {$a$}; \node at (1,2) [vertex] {}; \node at (1,2) [left] {$b$}; \node at (2,1) [vertex] {}; \node at (2,1) [right] {$c$}; \node at (2,2) [vertex] {}; \node at (2,2) [right] {$d$}; \node at (1.5, 0.5) {$X_1 \cup X_2$}; \end{tikzpicture} \end{document}
example_30013_combination_1
\documentclass[reqno]{amsart} \usepackage{amssymb} \usepackage{amsmath} \usepackage{tikz} \usepackage{color} \tikzset{vertex/.style={fill,circle,inner sep=1.0pt}} \begin{document} \begin{tikzpicture} \node at (1,1) [vertex] {}; \node at (1,1) [left] {$a$}; \end{tikzpicture} \end{document}
example_30013_main
\documentclass[reqno]{amsart} \usepackage{amssymb} \usepackage{amsmath} \usepackage{tikz} \usepackage{color} \tikzset{vertex/.style={fill,circle,inner sep=1.0pt}} \begin{document} \begin{tikzpicture} \node at (1,1) [vertex] {}; \node at (1,1) [left] {$a$}; \node at (1,2) [vertex] {}; \node at (1,2) [left] {$b$}; \node at (2,1) [vertex] {}; \node at (2,1) [right] {$c$}; \node at (2,2) [vertex] {}; \node at (2,2) [right] {$d$}; \node at (1.5, 0.5) {$X_1 \cup X_2$}; \end{tikzpicture} \end{document}
example_30014_combination_4
\documentclass[reqno]{amsart} \usepackage{amssymb} \usepackage{amsmath} \usepackage{tikz} \usepackage{color} \tikzset{vertex/.style={fill,circle,inner sep=1.0pt}} \newcommand{\dlK}[1]{\mathrm{dl}_K (#1)} \begin{document} \begin{tikzpicture} \node at (-0.865, 1) [vertex] {}; \node at (-0.865,0) [vertex] {}; \node at (0,0.5) [vertex] {}; \node at (0.865, 1) [vertex] {}; \end{tikzpicture} \end{document}
example_30014_combination_3
\documentclass[reqno]{amsart} \usepackage{amssymb} \usepackage{amsmath} \usepackage{tikz} \usepackage{color} \tikzset{vertex/.style={fill,circle,inner sep=1.0pt}} \newcommand{\dlK}[1]{\mathrm{dl}_K (#1)} \begin{document} \begin{tikzpicture} \node at (-0.865, 1) [vertex] {}; \node at (-0.865,0) [vertex] {}; \node at (0,0.5) [vertex] {}; \end{tikzpicture} \end{document}
example_30014_combination_2
\documentclass[reqno]{amsart} \usepackage{amssymb} \usepackage{amsmath} \usepackage{tikz} \usepackage{color} \tikzset{vertex/.style={fill,circle,inner sep=1.0pt}} \newcommand{\dlK}[1]{\mathrm{dl}_K (#1)} \begin{document} \begin{tikzpicture} \node at (-0.865, 1) [vertex] {}; \node at (-0.865,0) [vertex] {}; \end{tikzpicture} \end{document}
example_30014_combination_5
\documentclass[reqno]{amsart} \usepackage{amssymb} \usepackage{amsmath} \usepackage{tikz} \usepackage{color} \tikzset{vertex/.style={fill,circle,inner sep=1.0pt}} \newcommand{\dlK}[1]{\mathrm{dl}_K (#1)} \begin{document} \begin{tikzpicture} \node at (-0.865, 1) [vertex] {}; \node at (-0.865,0) [vertex] {}; \node at (0,0.5) [vertex] {}; \node at (0.865, 1) [vertex] {}; \node at (0.865,0) [vertex] {}; \end{tikzpicture} \end{document}
example_30014_combination_8
\documentclass[reqno]{amsart} \usepackage{amssymb} \usepackage{amsmath} \usepackage{tikz} \usepackage{color} \tikzset{vertex/.style={fill,circle,inner sep=1.0pt}} \newcommand{\dlK}[1]{\mathrm{dl}_K (#1)} \begin{document} \begin{tikzpicture} \node at (-0.865, 1) [vertex] {}; \node at (-0.865,0) [vertex] {}; \node at (0,0.5) [vertex] {}; \node at (0.865, 1) [vertex] {}; \node at (0.865,0) [vertex] {}; \fill [opacity=0.3] (0,0.5)--(-0.865,1)--(-0.865,0)--cycle (0,0.5)--(0.865,0)--(0.865,1)--cycle; \draw (0,0.5)--(-0.865,1)--(-0.865,0)--cycle (0,0.5)--(0.865,0)--(0.865,1)--cycle; \node at (-0.865, 1) [left] {$a$}; \node at (-0.865,0) [left] {$b$}; \end{tikzpicture} \end{document}
example_30014_combination_10
\documentclass[reqno]{amsart} \usepackage{amssymb} \usepackage{amsmath} \usepackage{tikz} \usepackage{color} \tikzset{vertex/.style={fill,circle,inner sep=1.0pt}} \newcommand{\dlK}[1]{\mathrm{dl}_K (#1)} \begin{document} \begin{tikzpicture} \node at (-0.865, 1) [vertex] {}; \node at (-0.865,0) [vertex] {}; \node at (0,0.5) [vertex] {}; \node at (0.865, 1) [vertex] {}; \node at (0.865,0) [vertex] {}; \fill [opacity=0.3] (0,0.5)--(-0.865,1)--(-0.865,0)--cycle (0,0.5)--(0.865,0)--(0.865,1)--cycle; \draw (0,0.5)--(-0.865,1)--(-0.865,0)--cycle (0,0.5)--(0.865,0)--(0.865,1)--cycle; \node at (-0.865, 1) [left] {$a$}; \node at (-0.865,0) [left] {$b$}; \node at (0,0.5) [above] {$u$}; \node at (0.865, 1) [right] {$d$}; \end{tikzpicture} \end{document}
example_30014_combination_6
\documentclass[reqno]{amsart} \usepackage{amssymb} \usepackage{amsmath} \usepackage{tikz} \usepackage{color} \tikzset{vertex/.style={fill,circle,inner sep=1.0pt}} \newcommand{\dlK}[1]{\mathrm{dl}_K (#1)} \begin{document} \begin{tikzpicture} \node at (-0.865, 1) [vertex] {}; \node at (-0.865,0) [vertex] {}; \node at (0,0.5) [vertex] {}; \node at (0.865, 1) [vertex] {}; \node at (0.865,0) [vertex] {}; \fill [opacity=0.3] (0,0.5)--(-0.865,1)--(-0.865,0)--cycle (0,0.5)--(0.865,0)--(0.865,1)--cycle; \end{tikzpicture} \end{document}
example_30014_combination_1
\documentclass[reqno]{amsart} \usepackage{amssymb} \usepackage{amsmath} \usepackage{tikz} \usepackage{color} \tikzset{vertex/.style={fill,circle,inner sep=1.0pt}} \newcommand{\dlK}[1]{\mathrm{dl}_K (#1)} \begin{document} \begin{tikzpicture} \node at (-0.865, 1) [vertex] {}; \end{tikzpicture} \end{document}
example_30014_combination_7
\documentclass[reqno]{amsart} \usepackage{amssymb} \usepackage{amsmath} \usepackage{tikz} \usepackage{color} \tikzset{vertex/.style={fill,circle,inner sep=1.0pt}} \newcommand{\dlK}[1]{\mathrm{dl}_K (#1)} \begin{document} \begin{tikzpicture} \node at (-0.865, 1) [vertex] {}; \node at (-0.865,0) [vertex] {}; \node at (0,0.5) [vertex] {}; \node at (0.865, 1) [vertex] {}; \node at (0.865,0) [vertex] {}; \fill [opacity=0.3] (0,0.5)--(-0.865,1)--(-0.865,0)--cycle (0,0.5)--(0.865,0)--(0.865,1)--cycle; \draw (0,0.5)--(-0.865,1)--(-0.865,0)--cycle (0,0.5)--(0.865,0)--(0.865,1)--cycle; \node at (-0.865, 1) [left] {$a$}; \end{tikzpicture} \end{document}
example_30014_combination_9
\documentclass[reqno]{amsart} \usepackage{amssymb} \usepackage{amsmath} \usepackage{tikz} \usepackage{color} \tikzset{vertex/.style={fill,circle,inner sep=1.0pt}} \newcommand{\dlK}[1]{\mathrm{dl}_K (#1)} \begin{document} \begin{tikzpicture} \node at (-0.865, 1) [vertex] {}; \node at (-0.865,0) [vertex] {}; \node at (0,0.5) [vertex] {}; \node at (0.865, 1) [vertex] {}; \node at (0.865,0) [vertex] {}; \fill [opacity=0.3] (0,0.5)--(-0.865,1)--(-0.865,0)--cycle (0,0.5)--(0.865,0)--(0.865,1)--cycle; \draw (0,0.5)--(-0.865,1)--(-0.865,0)--cycle (0,0.5)--(0.865,0)--(0.865,1)--cycle; \node at (-0.865, 1) [left] {$a$}; \node at (-0.865,0) [left] {$b$}; \node at (0,0.5) [above] {$u$}; \end{tikzpicture} \end{document}
example_30014_main
\documentclass[reqno]{amsart} \usepackage{amssymb} \usepackage{amsmath} \usepackage{tikz} \usepackage{color} \tikzset{vertex/.style={fill,circle,inner sep=1.0pt}} \newcommand{\dlK}[1]{\mathrm{dl}_K (#1)} \begin{document} \begin{tikzpicture} \node at (-0.865, 1) [vertex] {}; \node at (-0.865,0) [vertex] {}; \node at (0,0.5) [vertex] {}; \node at (0.865, 1) [vertex] {}; \node at (0.865,0) [vertex] {}; \fill [opacity=0.3] (0,0.5)--(-0.865,1)--(-0.865,0)--cycle (0,0.5)--(0.865,0)--(0.865,1)--cycle; \draw (0,0.5)--(-0.865,1)--(-0.865,0)--cycle (0,0.5)--(0.865,0)--(0.865,1)--cycle; \node at (-0.865, 1) [left] {$a$}; \node at (-0.865,0) [left] {$b$}; \node at (0,0.5) [above] {$u$}; \node at (0.865, 1) [right] {$d$}; \node at (0.865,0) [right] {$c$}; \node at (0,-1) {$\dlK{v}$}; \end{tikzpicture} \end{document}
example_30015_combination_5
\documentclass[reqno]{amsart} \usepackage{amssymb} \usepackage{amsmath} \usepackage{tikz} \usepackage{color} \tikzset{vertex/.style={fill,circle,inner sep=1.0pt}} \newcommand{\lkK}[1]{\mathrm{lk}_K (#1)} \begin{document} \begin{tikzpicture} \node at (-0.865,0) [vertex] {}; \node at (0,0.5) [vertex] {}; \node at (0.865,0) [vertex] {}; \draw (0,0.5)--(-0.865,0) (0,0.5)--(0.865,0); \node at (-0.865,0) [left] {$b$}; \end{tikzpicture} \end{document}
example_30015_combination_2
\documentclass[reqno]{amsart} \usepackage{amssymb} \usepackage{amsmath} \usepackage{tikz} \usepackage{color} \tikzset{vertex/.style={fill,circle,inner sep=1.0pt}} \newcommand{\lkK}[1]{\mathrm{lk}_K (#1)} \begin{document} \begin{tikzpicture} \node at (-0.865,0) [vertex] {}; \node at (0,0.5) [vertex] {}; \end{tikzpicture} \end{document}
example_30015_combination_3
\documentclass[reqno]{amsart} \usepackage{amssymb} \usepackage{amsmath} \usepackage{tikz} \usepackage{color} \tikzset{vertex/.style={fill,circle,inner sep=1.0pt}} \newcommand{\lkK}[1]{\mathrm{lk}_K (#1)} \begin{document} \begin{tikzpicture} \node at (-0.865,0) [vertex] {}; \node at (0,0.5) [vertex] {}; \node at (0.865,0) [vertex] {}; \end{tikzpicture} \end{document}
example_30015_combination_4
\documentclass[reqno]{amsart} \usepackage{amssymb} \usepackage{amsmath} \usepackage{tikz} \usepackage{color} \tikzset{vertex/.style={fill,circle,inner sep=1.0pt}} \newcommand{\lkK}[1]{\mathrm{lk}_K (#1)} \begin{document} \begin{tikzpicture} \node at (-0.865,0) [vertex] {}; \node at (0,0.5) [vertex] {}; \node at (0.865,0) [vertex] {}; \draw (0,0.5)--(-0.865,0) (0,0.5)--(0.865,0); \end{tikzpicture} \end{document}
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