AdmissibleInversions on Permutation
Pairs i < j with p(i) > p(j) and either p(i-1) < p(i) or some entry between them larger than p(i).
FindStat's St000866 is the Shareshian-Wachs version, which differs.
Called as CombinatorialStat(x, "AdmissibleInversions"). The head's page has its examples.
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FindStat St000463
The number of admissible inversions of a permutation.
| Object | Value |
|---|---|
[] | 0 |
[1] | 0 |
[1,2] | 0 |
[2,1] | 0 |
[1,2,3] | 0 |
[1,3,2] | 1 |
[2,1,3] | 0 |
[2,3,1] | 2 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000463 has the rest.