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ThreeExcedances on Permutation ​

Positions with p(i) = i + 3.

On Permutation

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

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Distribution

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FindStat St000649

The number of 3-excedences of a permutation.

ObjectValue
[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
[3,2,1]0

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000649 has the rest.