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OverlapSetSize on Permutation ​

Shifts i < n for which the first n - i entries and the last n - i entries are in the same relative order.

On Permutation

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

Live

Distribution

Over SymmetricGroup at each size, tallied here in your browser; sizes past 8 are not offered.

FindStat St001096

The size of the overlap set of a permutation.

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

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001096 has the rest.