74 lines
1.9 KiB
TeX
74 lines
1.9 KiB
TeX
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\documentclass[12pt,a4paper,german]{article}
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\usepackage{url}
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%\usepackage{graphics}
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\usepackage{times}
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\usepackage[T1]{fontenc}
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\usepackage{ngerman}
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\usepackage{float}
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\usepackage{diagbox}
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\usepackage[utf8]{inputenc}
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\usepackage{geometry}
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\usepackage{amsfonts}
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\usepackage{amsmath}
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\usepackage{csquotes}
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\usepackage{graphicx}
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\usepackage{epsfig}
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\usepackage{paralist}
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\geometry{left=2.0cm,textwidth=17cm,top=3.5cm,textheight=23cm}
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%%%%%%%%%% Fill out the the definitions %%%%%%%%%
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\def \name {Valentin Brandl} %
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\def \matrikel {108018274494} %
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\def \pname {Marvin Herrmann} %
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\def \pmatrikel {108018265436} %
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\def \gruppe {2 (Mi 10-12 Andre)}
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\def \uebung {2} %
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% DO NOT MODIFY THIS HEADER
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\newcommand{\hwsol}{
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\vspace*{-2cm}
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\noindent \matrikel \quad \name \hfill \"Ubungsgruppe: \gruppe \\
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\noindent \pmatrikel \quad \pname \\
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\begin{center}{\Large \bf L\"osung f\"ur \"Ubung \# \uebung}\end{center}
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}
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\begin{document}
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%Import header
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\hwsol
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\section*{Aufgabe 2.2}
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\begin{enumerate}[1.]
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\item Zyklenzerlegung: $(1\ 2\ 4) (3) (5\ 9) (6) (7\ 8)$
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2 Fixpunkte: $3$ und $6$
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\item
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\begin{tabular}{c|cccccccccc}
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$n / k$ & 0&1&2&3&4&5&6&7&8&9 \\\hline
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0 & 1 &&&&&&&&& \\
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1 & 0 & 1 &&&&&&&& \\
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2 & 0 & 1 &1&&&&&&& \\
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3 & 0 & 2 & 3 & 1 & & & & & & \\
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4 & 0 & 6 & 11 & 6 & 1 & & & & & \\
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5 & 0 & 24 & 50 & 35 & 10 & 1 & & & & \\
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6 & 0 & 120 & 274 & 225 & 85 & 15 & 1 & & & \\
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7 & 0 & 720 & 1764 & 1624 & 735 & 175 & 21 & 1 & & \\
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8 & 0 & 5040 & 13068 & 13132 & 6769 & 1960 & 322 & 28 & 1 & \\
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9 & 0 & 40320 & 109584 & 118124 & 67284 & \underline{22449} & 4536 & 546 & 36 & 1 \\
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\end{tabular}
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\begin{eqnarray*}
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s_{n.k} &=& s_{n-1,k-1} + (n-1)s_{n-1,k} \text{ mit} \\
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s_{0,0} &=& 1 \\
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s_{n,0} &=& 0 \\
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s_{n,n} &=& 1 \\\\
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s_{9,5} &=& 22449
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\end{eqnarray*}
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\end{enumerate}
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\end{document}
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