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FixedPoints on Permutation ​

Positions with p(i) = i.

On Permutation

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

Live

FindStat St000022

The number of fixed points of a permutation.

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

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000022 has the rest.