ConjugacyClassSize on Permutation
The number of permutations of the same cycle type: n! over the product of the cycle sizes and the factorials of the multiplicities.
Called as CombinatorialStat(x, "ConjugacyClassSize"). The head's page has its examples.
Live
Distribution
Over SymmetricGroup at each size, tallied here in your browser; sizes past 8 are not offered.
Also on
The same name on other carriers, each its own implementation: IntegerPartition.
FindStat St000690
The size of the conjugacy class of a permutation.
| Object | Value |
|---|---|
[1,2] | 1 |
[2,1] | 1 |
[1,2,3] | 1 |
[1,3,2] | 3 |
[2,1,3] | 3 |
[2,3,1] | 2 |
[3,1,2] | 2 |
[3,2,1] | 3 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000690 has the rest.