I have the permutation $\pi $, that satisfies $\pi = \pi^{-1} $. Then $\pi $ is probably an indentical permutation. Is it all, or are there another permutations that satisfy my task?
Finding the permutations satisfying $\pi = \pi^{-1}$
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$\begingroup$
linear-algebra
permutations
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0How about transpositions? – 2017-02-12
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0Or any product of disjoint transpositions. – 2017-02-12
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0I am not sure how do you mean it. – 2017-02-12
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0Do you know what a transposition is? – 2017-02-12
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0Are you familiar with cycle notation? What carmichael561 was saying was that a cycle like $(1 2)$ satisfies your equation. What I added was that a product of two cycles $(1 2)(3 4)$ also satsifies $\pi = \pi ^{-1}$. – 2017-02-12
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0Oh, I see. Thank you. – 2017-02-12
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0Write $\pi$ as a product of disjoint cycles. – 2017-02-12
1 Answers
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Any product of disjoint 2-cycles will have this property.