Inverse and Cyclic Permutations with Examples

In this class, We discuss Inverse and Cyclic Permutations with Examples.

The reader should have prior knowledge of permutations. Click Here.

Inverse Permutation:

Given a permutation P, there exists a permutation P’ such that PoP’ = P’oP = I

I mean, identity permutation

Example:

The diagram below will show the inverse of a permutation.

Cyclic permutation:

A permutation that replaces n objects cyclically is called a cyclic or circular permutation.

The diagram below shows the cyclic permutation examples.

A cycle of length two is called transposition.

The below diagram shows how to write cyclic permutations in transposition.

Even permutation:

A permutation that has an even number of transpositions is called an even permutation.

The diagram below shows the even permutation.

Odd Permutation:

A permutation that has an odd number of transpositions is called an odd permutation.

The diagram below shows the odd permutation.