LongestCycleLength on Permutation

The size of the largest cycle (the catalog's second spelling).

On Permutation

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

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Distribution

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Sizes 1 to

FindStat St000485

The length of the longest cycle of a permutation.

Object	Value
[1,2]	1
[2,1]	2
[1,2,3]	1
[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/St000485 has the rest.