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DoubleExcedances on Permutation ​

Positions with i < p(i) < p(p(i)).

On Permutation

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

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Distribution

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FindStat St000731

The number of double exceedences of a permutation.

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

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000731 has the rest.