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author | Andreas Müller <andreas.mueller@ost.ch> | 2021-02-09 21:52:16 +0100 |
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committer | Andreas Müller <andreas.mueller@ost.ch> | 2021-02-09 21:52:16 +0100 |
commit | ada53a9c225b896c8d7608300427aac475bb7045 (patch) | |
tree | 1b1fe99c3e78256ff839611225dd61d983b96575 /buch/chapters/50-permutationen/transpositionen.tex | |
parent | Illustrationen Markov-Ketten (diff) | |
download | SeminarMatrizen-ada53a9c225b896c8d7608300427aac475bb7045.tar.gz SeminarMatrizen-ada53a9c225b896c8d7608300427aac475bb7045.zip |
move all iamges to separate files
Diffstat (limited to 'buch/chapters/50-permutationen/transpositionen.tex')
-rw-r--r-- | buch/chapters/50-permutationen/transpositionen.tex | 87 |
1 files changed, 1 insertions, 86 deletions
diff --git a/buch/chapters/50-permutationen/transpositionen.tex b/buch/chapters/50-permutationen/transpositionen.tex index baed2fb..604e010 100644 --- a/buch/chapters/50-permutationen/transpositionen.tex +++ b/buch/chapters/50-permutationen/transpositionen.tex @@ -35,92 +35,7 @@ also die Permutation, die $1\to2\to3\to\dots\to k-2\to k-1\to k\to 1$ abbildet. Dieser Zyklus lässt sich wie folgt aus Transpositionen zusammensetzen: \begin{center} -\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] -\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} +\includegraphics{chapters/50-permutationen/images/transpositionen.pdf} \end{center} Es ist also \[ |