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PermutationSupport on Permutation ​

The points p moves, in increasing order.

On Permutation

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

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Distribution

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

FindStat St000673

The number of non-fixed points of a permutation.

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

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000673 has the rest.