CubeRootCount on IntegerPartition
The permutations whose cube is a fixed permutation of this cycle type: the product over part sizes d, with a parts of size d, of the number of ways to take the cube root of each part of size d alone or of three together as a cycle of length 3d.
Called as CombinatorialStat(x, "CubeRootCount"). 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.
FindStat St001364
The number of permutations whose cube equals a fixed permutation of given cycle type.
| Object | Value |
|---|---|
[1] | 1 |
[2] | 1 |
[3] | 0 |
[4] | 1 |
[5] | 1 |
[6] | 0 |
[7] | 1 |
[8] | 1 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001364 has the rest.