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DescentsOfDistanceThree on Permutation ​

Positions i with p(i) > p(i+3).

On Permutation

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

Live

Distribution

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FindStat St001520

The number of strict 3-descents.

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/St001520 has the rest.