IncreasingPositivePairCount on SignedPermutation
Pairs i < j with 0 < p(i) < p(j): the occurrences of the signed pattern 12.
FindStat's St001772. Both entries positive and increasing.
Called as CombinatorialStat(x, "IncreasingPositivePairCount"). The head's page has its examples.
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Distribution
Over SignedPermutations at each size, tallied here in your browser; sizes past 6 are not offered.
FindStat St001772
The number of occurrences of the signed pattern 12 in a signed permutation.
| Object | Value |
|---|---|
[1] | 0 |
[-1] | 0 |
[1,2] | 1 |
[2,1] | 0 |
[-1,2] | 0 |
[-2,1] | 0 |
[1,-2] | 0 |
[2,-1] | 0 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001772 has the rest.