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CyclicSmallExcedances on Permutation ​

Positions with p(i) = i + 1, read cyclically: the last position counts when p(n) = 1.

On Permutation

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

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Distribution

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FindStat St000241

The number of cyclical small excedances.

ObjectValue
[1]1
[1,2]0
[2,1]2
[1,2,3]0
[1,3,2]1
[2,1,3]1
[2,3,1]3
[3,1,2]0

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000241 has the rest.