Inverse and Cyclic Permutations with Examples || Lesson 82 || Discrete Math & Graph Theory ||

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.

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[harshavardhan-cgms]

Thanks a lot it helped me at my exam 😭❤️