InvariantSubsetCount on IntegerPartition

Subsets of the points left invariant by a permutation with these cycle lengths: each cycle is in or out, 2 to the number of cycles.

On IntegerPartition

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

Live

Distribution

Over IntegerPartitions at each size, tallied here in your browser; sizes past 30 are not offered.

Sizes 1 to

FindStat St000511

The number of invariant subsets when acting with a permutation of given cycle type.

Object	Value
[]	1
[1]	2
[2]	2
[3]	2
[4]	2
[5]	2
[6]	2
[7]	2

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000511 has the rest.