BruhatTranspositionCount on Permutation
Transpositions that are at most p in Bruhat order.
Equal to the inversions exactly when p avoids 4231 and 3412.
Called as CombinatorialStat(x, "BruhatTranspositionCount"). The head's page has its examples.
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FindStat St001558
The number of transpositions that are smaller or equal to a permutation in Bruhat order.
| Object | Value |
|---|---|
[1] | 0 |
[1,2] | 0 |
[2,1] | 1 |
[1,2,3] | 0 |
[1,3,2] | 1 |
[2,1,3] | 1 |
[2,3,1] | 2 |
[3,1,2] | 2 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001558 has the rest.