PositiveBeforeNegativeCount on SignedPermutation
Twice the adjacent pairs of a positive entry followed by a negative one, plus 1 when the first entry is negative.
FindStat's St001870 counts them in the word p(-n), ..., p(-1), p(1), ..., p(n) with p(-i) = -p(i): each adjacent pair twice, once reflected, and the pair across the middle when p(1) is negative.
Called as CombinatorialStat(x, "PositiveBeforeNegativeCount"). 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 St001870
The number of positive entries followed by a negative entry in a signed permutation.
| Object | Value |
|---|---|
[1] | 0 |
[-1] | 1 |
[1,2] | 0 |
[2,1] | 0 |
[-1,2] | 1 |
[-2,1] | 1 |
[1,-2] | 2 |
[2,-1] | 2 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001870 has the rest.