InvariantOrientedCycleCount on IntegerPartition
The cyclic permutations that a permutation of this cycle type fixes under conjugation: none unless the parts are all equal to some d, in which case totient(d) d^(m-1) (m-1)! for m parts.
Called as CombinatorialStat(x, "InvariantOrientedCycleCount"). 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 St000510
The number of invariant oriented cycles when acting with a permutation of given cycle type.
| Object | Value |
|---|---|
[2] | 1 |
[3] | 2 |
[4] | 2 |
[5] | 4 |
[6] | 2 |
[7] | 6 |
[8] | 4 |
[9] | 6 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000510 has the rest.