TypeBInversionCount on SignedPermutation
Pairs i < j with p(i) > p(j), plus pairs i <= j with -p(i) > p(j).
The Coxeter length in type B (FindStat St001428).
Called as CombinatorialStat(x, "TypeBInversionCount"). 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 St001428
The number of B-inversions of a signed permutation.
| Object | Value |
|---|---|
[1] | 0 |
[-1] | 1 |
[1,2] | 0 |
[2,1] | 1 |
[-1,2] | 1 |
[-2,1] | 2 |
[1,-2] | 3 |
[2,-1] | 2 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001428 has the rest.