InverseByConjugationCount on IntegerPartition
The permutations that a fixed permutation of this cycle type conjugates to their inverse: the square roots of its square, a product over the cycle lengths d of the roots of the cycles of length d.
alpha pi alpha^-1 = pi^-1 exactly when (pi alpha)^2 = alpha^2.
Called as CombinatorialStat(x, "InverseByConjugationCount"). The head's page has its examples.
Live
Distribution
Over IntegerPartitions at each size, tallied here in your browser; sizes past 30 are not offered.
FindStat St001710
The number of permutations such that conjugation with a permutation of given cycle type yields the inverse permutation.
| Object | Value |
|---|---|
[] | 1 |
[1] | 1 |
[2] | 2 |
[3] | 1 |
[4] | 2 |
[5] | 1 |
[6] | 4 |
[7] | 1 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001710 has the rest.