For example, I have the following permutation:
P(3 4 1 2 5)
When I calculate the inverse of this permutation, I get the same result: (3 4 1 2 5)
Am I doing the calculation incorrect?
Can the inverse of a permutation be the same as itself?
1
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discrete-mathematics
permutations
1 Answers
3
No, you are doing it fine. Those kind of permutations are called Involutions. If you write the cycle decomposition of those you will see that cycles are just composed by $1$ or $2$ elements. In your case $$34125=(13)(24)(5).$$