Hag on Permutation

The excedance tops less their positions, plus the inversions among the excedance tops less those among the rest, plus the pairs k < i, over excedances i, with p(k) <= i.

On Permutation

FindStat's Haglund hag. The inversions are within the subwords, as in Denert.

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

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Distribution

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Sizes 1 to

FindStat St001671

Haglund's hag 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]	2

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001671 has the rest.