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LargestDirectSummandSize on Permutation ​

The size of the largest block of p as a direct sum.

On Permutation

Called as CombinatorialStat(x, "LargestDirectSummandSize"). 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 St000844

The size of the largest block in the direct sum decomposition of a permutation.

ObjectValue
[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]3

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000844 has the rest.