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| -rw-r--r-- | buch/chapters/50-permutationen/images/transpositionen.tex | 103 |
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diff --git a/buch/chapters/50-permutationen/images/transpositionen.tex b/buch/chapters/50-permutationen/images/transpositionen.tex new file mode 100644 index 0000000..0670a2c --- /dev/null +++ b/buch/chapters/50-permutationen/images/transpositionen.tex @@ -0,0 +1,103 @@ +% +% transpositionen.tex -- Darstellung eines Zyklus aus Transpositionen +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\documentclass[tikz]{standalone} +\usepackage{amsmath} +\usepackage{times} +\usepackage{txfonts} +\usepackage{pgfplots} +\usepackage{csvsimple} +\usetikzlibrary{arrows,intersections,math} +\begin{document} +\def\skala{1} + +\def\kreuz#1#2#3{ + \draw[->] ({(#1)-1},#2) to[out=-90,in=90] ({#1},{#2-1}); + \draw[->] ({#1},#2) to[out=-90,in=90] ({#1-1},{#2-1}); + \node at ({(#1)-0.5+0.2},{#2-0.5}) [right] {$#3$}; +} +\begin{tikzpicture}[>=latex,thick,scale=\skala] +\foreach \x in {1,2,3,6,7,8,9}{ + \fill ({\x-1},0) circle[radius=0.05]; +} +\foreach \x in {1,2,3}{ + \node at ({\x-1},0) [above] {$\tiny \x$}; +} +\node at (8,0) [above] {$\tiny k$}; +\node at (7,0) [above] {$\tiny k-1$}; +\node at (6,0) [above] {$\tiny k-2$}; +\node at (5,0) [above] {$\tiny k-3$}; +\foreach \x in {1,2,3,4,7,8,9}{ + \fill ({\x-1},-8) circle[radius=0.05]; +} +\foreach \x in {1,2,3,4}{ + \node at ({\x-1},-8) [below] {$\tiny \x$}; +} +\node at (6,-8) [below] {$k-2$}; +\node at (7,-8) [below] {$k-1$}; +\node at (8,-8) [below] {$k$}; + +\foreach \x in {3,3.2,...,5}{ + \fill (\x,{-8+\x}) circle[radius=0.02]; + \fill ({\x+0.5},-8) circle[radius=0.02]; + \fill ({\x-0.5},0) circle[radius=0.02]; +} + +\kreuz{8}{0}{\tau_{k-1,k}} +\kreuz{7}{-1}{\tau_{k-2,k-1}} +\kreuz{6}{-2}{\tau_{k-3,k-2}} +%\kreuz{5}{-3}{\tau_{56}} +%\kreuz{4}{-4}{\tau_{45}} +\kreuz{3}{-5}{\tau_{34}} +\kreuz{2}{-6}{\tau_{23}} +\kreuz{1}{-7}{\tau_{12}} + +\draw[->,color=gray] (0,0) -- (0,-7); +\draw[->,color=gray] (1,0) -- (1,-6); +\draw[->,color=gray] (2,0) -- (2,-5); +%\draw[->,color=gray] (3,0) -- (3,-4); +%\draw[->,color=gray] (4,0) -- (4,-3); +\draw[->,color=gray] (5,0) -- (5,-2); +\draw[->,color=gray] (6,0) -- (6,-1); + +\draw[->,color=gray] (8,-1) -- (8,-8); +\draw[->,color=gray] (7,-2) -- (7,-8); +\draw[->,color=gray] (6,-3) -- (6,-8); +%\draw[->,color=gray] (5,-4) -- (5,-8); +%\draw[->,color=gray] (4,-5) -- (4,-8); +\draw[->,color=gray] (3,-6) -- (3,-8); +\draw[->,color=gray] (2,-7) -- (2,-8); + +\fill (6,-1) circle[radius=0.05]; +\fill (7,-1) circle[radius=0.05]; +\fill (8,-1) circle[radius=0.05]; + +\fill (5,-2) circle[radius=0.05]; +\fill (6,-2) circle[radius=0.05]; +\fill (7,-2) circle[radius=0.05]; + +%\fill (4,-3) circle[radius=0.05]; +\fill (5,-3) circle[radius=0.05]; +\fill (6,-3) circle[radius=0.05]; + +%\fill (3,-4) circle[radius=0.05]; +%\fill (4,-4) circle[radius=0.05]; +%\fill (5,-4) circle[radius=0.05]; + +\fill (2,-5) circle[radius=0.05]; +\fill (3,-5) circle[radius=0.05]; +%\fill (4,-5) circle[radius=0.05]; + +\fill (1,-6) circle[radius=0.05]; +\fill (2,-6) circle[radius=0.05]; +\fill (3,-6) circle[radius=0.05]; + +\fill (0,-7) circle[radius=0.05]; +\fill (1,-7) circle[radius=0.05]; +\fill (2,-7) circle[radius=0.05]; + +\end{tikzpicture} +\end{document} + |