HalfSymmetryClassSize on Permutation

Half the size of the symmetry class of p, rounded down.

On Permutation

The symmetry class is generated by inverse, reverse and complement.

Called as CombinatorialStat(x, "HalfSymmetryClassSize"). 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.

Sizes 1 to

FindStat St000402

Half the size of the symmetry class of a permutation.

Object	Value
[1,2]	1
[2,1]	1
[1,2,3]	1
[1,3,2]	2
[2,1,3]	2
[2,3,1]	2
[3,1,2]	2
[3,2,1]	1

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000402 has the rest.