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SmallestFixedPoint on Permutation ​

The smallest i with p(i) = i, or n + 1 when there is none.

On Permutation

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

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Distribution

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FindStat St001468

The smallest fixpoint of a permutation.

ObjectValue
[1]1
[1,2]1
[2,1]3
[1,2,3]1
[1,3,2]1
[2,1,3]3
[2,3,1]4
[3,1,2]4

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001468 has the rest.