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BruhatLowerCovers on Permutation ​

Pairs i < j with p(i) > p(j) and no entry between them valued between p(j) and p(i).

On Permutation

The boxed occurrences of 21.

Called as CombinatorialStat(x, "BruhatLowerCovers"). The head's page has its examples.

Live

Distribution

Over SymmetricGroup at each size, tallied here in your browser; sizes past 8 are not offered.

FindStat St000957

The number of Bruhat lower covers of a permutation.

ObjectValue
[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
[3,2,1]2

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000957 has the rest.