SignedReflectionLength on SignedPermutation
The least number of reflections of the hyperoctahedral group with product p: n minus the positive cycles.
FindStat's St001769. The codimension of the fixed space, which is n less the number of positive cycles. Not ReflectionLength, which counts transpositions of an unsigned permutation.
Called as CombinatorialStat(x, "SignedReflectionLength"). The head's page has its examples.
Live
Distribution
Over SignedPermutations at each size, tallied here in your browser; sizes past 6 are not offered.
FindStat St001769
The reflection length of a signed permutation.
| Object | Value |
|---|---|
[1] | 0 |
[-1] | 1 |
[1,2] | 0 |
[2,1] | 1 |
[-1,2] | 1 |
[-2,1] | 2 |
[1,-2] | 1 |
[2,-1] | 2 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001769 has the rest.