SymmetryClassSize on Permutation
The permutations reachable from p by inverse, reverse and complement: 8 over the symmetries that fix p.
Called as CombinatorialStat(x, "SymmetryClassSize"). 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.
FindStat St000401
The size of the symmetry class of a permutation.
| Object | Value |
|---|---|
[1] | 1 |
[1,2] | 2 |
[2,1] | 2 |
[1,2,3] | 2 |
[1,3,2] | 4 |
[2,1,3] | 4 |
[2,3,1] | 4 |
[3,1,2] | 4 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000401 has the rest.