PermutationGenus on Permutation
The genus g with n + 1 - 2g the cycles of p plus the cycles of p^-1 composed with the long cycle.
Called as CombinatorialStat(x, "PermutationGenus"). 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 St001394
The genus of a permutation.
| Object | Value |
|---|---|
[1] | 0 |
[1,2] | 0 |
[2,1] | 0 |
[1,2,3] | 0 |
[1,3,2] | 0 |
[2,1,3] | 0 |
[2,3,1] | 0 |
[3,1,2] | 1 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001394 has the rest.