BruhatNonInversionTranspositionCount on Permutation
Transpositions at most p in Bruhat order that are not inversions of p.
Zero exactly when p is smooth, avoiding 4231 and 3412.
Called as CombinatorialStat(x, "BruhatNonInversionTranspositionCount"). The head's page has its examples.
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FindStat St001559
The number of transpositions that are smaller or equal to a permutation in Bruhat order while not being inversions.
| Object | Value |
|---|---|
[1] | 0 |
[1,2] | 0 |
[2,1] | 0 |
[1,2,3] | 0 |
[1,3,2] | 0 |
[2,1,3] | 0 |
[2,3,1] | 0 |
[3,1,2] | 0 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001559 has the rest.