Denert on Permutation
Sum of the excedance positions, plus the inversions within each of the excedance and non-excedance subwords.
Foata–Zeilberger's den (FindStat St000156). Mahonian, and (Excedances, Denert) is equidistributed with (Descents, MajorIndex) — checked in tests/permutation.test.ts. Moved off the frontier: it needs no fold, just same-block inversion counting.
Called as CombinatorialStat(x, "Denert"). The head's page has its examples.
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FindStat St000156
The Denert index of a permutation.
| Object | Value |
|---|---|
[1] | 0 |
[1,2] | 0 |
[2,1] | 1 |
[1,2,3] | 0 |
[1,3,2] | 2 |
[2,1,3] | 1 |
[2,3,1] | 3 |
[3,1,2] | 1 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000156 has the rest.