FlagDescent on SignedPermutation

Twice the descents between entries, plus 1 when the first entry is negative.

On SignedPermutation

FindStat's St001893. The descent at 0 counts once, the others twice.

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

Sizes 1 to

FindStat St001893

The flag descent of a signed permutation.

Object	Value
[1]	0
[-1]	1
[1,2]	0
[2,1]	2
[-1,2]	1
[-2,1]	1
[1,-2]	2
[2,-1]	2

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001893 has the rest.