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StrongFixedPoints on Permutation ​

Positions that are both a left-to-right maximum and a right-to-left minimum.

On Permutation

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

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Distribution

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FindStat St000221

The number of strong fixed points of a permutation.

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

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000221 has the rest.