Find number of square permutations

Asked Jul 11 '18 at 13:36

Active Jul 23 '18 at 08:39

Viewed 464 times

Let's call a permutation a square if it is a product of some other permutation with itself.

For a given $n$, find the number of square permutations.

Attempt

This question explains that a permutation has a square root if and only if the number of cycles of same even length in its representation is even (or zero). But how do we calculate the number of permutations with such a property?

edited Jul 23 '18 at 08:39

Bilbottom

2,658
2
15
33

asked Jul 11 '18 at 13:36

Ignacio

4

The problem is not so obvious... have a look at this paper. – Théophile Jul 11 '18 at 13:59
1

There is an EGF at Wikipedia on random permutations. – Marko Riedel Jul 11 '18 at 14:06
2

Cheating: http://oeis.org/A003483 – Jul 11 '18 at 14:35

Find number of square permutations

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