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InvisibleInversions on Permutation ​

Pairs i < j with p(i) > p(j) > i.

On Permutation

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

Live

Distribution

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FindStat St001727

The number of invisible inversions of a permutation.

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]1

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001727 has the rest.