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CyclesOfLengthAtMostThree on Permutation ​

Cycles of size at most three.

On Permutation

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

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FindStat St000489

The number of cycles of a permutation of length at most 3.

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

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000489 has the rest.