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Mathematik-Online problems:

Problem 453: Permutations of a Set

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
Let $ d=(1\; 2\; 3\; 4)$ and $ s=(2\; 4)$ be permutations of the set $ \{1,2,3,4\}$.

a)
Interpret $ d$ and $ s$ as mappings of a square onto itself. What kind of mappings are $ d$ and $ s$?

b)
Is $ d \circ s = s \circ d$?

c)
Find all mappings that can be written as compositions of $ d$'s und $ s$'s. What kind of mappings are these?

d)
Does c) includes every permutation of $ \{1,2,3,4\}$?
(Authors: Höllig/Höfert)
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  automatisch erstellt am 12.  3. 2018