Permutationen/41352/Verschiedene Eigenschaften/Aufgabe/Lösung

a) ${\displaystyle {}\tau ^{2}}$ besitzt die Wertetabelle

${\displaystyle {}x}$	${\displaystyle {}1}$	${\displaystyle {}2}$	${\displaystyle {}3}$	${\displaystyle {}4}$	${\displaystyle {}5}$
${\displaystyle {}\tau (x)}$	${\displaystyle {}5}$	${\displaystyle {}4}$	${\displaystyle {}3}$	${\displaystyle {}2}$	${\displaystyle {}1}$

und ${\displaystyle {}\tau ^{2}}$ besitzt die Wertetabelle

${\displaystyle {}x}$	${\displaystyle {}1}$	${\displaystyle {}2}$	${\displaystyle {}3}$	${\displaystyle {}4}$	${\displaystyle {}5}$
${\displaystyle {}\tau (x)}$	${\displaystyle {}2}$	${\displaystyle {}5}$	${\displaystyle {}3}$	${\displaystyle {}1}$	${\displaystyle {}4}$

b) Die Fehlstände sind

${\displaystyle (1,2),\,(1,3),\,(1,5),\,(3,5),\,(4,5).}$

${\displaystyle {}5}$

${\displaystyle {}-1}$