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Separators on Permutation ​

The values v that are a vertical separator of p, or whose image under p^-1 is a vertical separator of p^-1.

On Permutation

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

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Distribution

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FindStat St001402

The number of separators in a permutation.

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

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001402 has the rest.