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InversionsBetweenExcedancesWithLinkedGreater on Permutation ​

Pairs i < j < p(j) < p(i) with p^-1(j) < j.

On Permutation

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

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Distribution

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FindStat St001550

The number of inversions between exceedances where the greater exceedance is linked.

ObjectValue
[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/St001550 has the rest.