Zu ${\displaystyle {}n\in \mathbb {N} }$ sei

${\displaystyle {}[n]=\{0,1,2,\ldots ,n\}\,.}$

Zu jedem ${\displaystyle {}n\in \mathbb {N} }$ und jedem ${\displaystyle {}0\leq k\leq n}$ seien die Abbildungen

${\displaystyle D_{k}\colon [n]\longrightarrow [n+1]}$

durch

${\displaystyle {}D_{k}(j)={\begin{cases}j,{\text{ falls }}j<k,\\j+1{\text{ sonst}},\end{cases}}\,}$

und die Abbildungen

${\displaystyle S_{k}\colon [n+1]\longrightarrow [n]}$

durch

${\displaystyle {}S_{k}(j)={\begin{cases}j,{\text{ falls }}j\leq k,\\j-1{\text{ sonst}},\end{cases}}\,}$

definiert.

a) Erstelle eine Wertetabelle für

${\displaystyle D_{3}\colon [4]\longrightarrow [5].}$

b) Erstelle eine Wertetabelle für

${\displaystyle S_{3}\colon [6]\longrightarrow [5].}$

c) Beschreibe die durch die Wertetabelle

${\displaystyle {}j}$	${\displaystyle {}0}$	${\displaystyle {}1}$	${\displaystyle {}2}$	${\displaystyle {}3}$	${\displaystyle {}4}$	${\displaystyle {}5}$
${\displaystyle {}\varphi (j)}$	${\displaystyle {}0}$	${\displaystyle {}2}$	${\displaystyle {}2}$	${\displaystyle {}4}$	${\displaystyle {}5}$	${\displaystyle {}5}$

${\displaystyle \varphi \colon [5]\longrightarrow [5]}$

${\displaystyle {}D_{k}}$

${\displaystyle {}S_{i}}$