BraceletCount on IntegerPartition
The colorings of a polygon with these color multiplicities, up to rotation and reflection: the necklaces and the colorings fixed by the reflections, over twice the size.
FindStat's St001603 (the dihedral group); its title says colourings of a polygon. It is only defined there for sizes of at least 3.
Called as CombinatorialStat(x, "BraceletCount"). 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 St001603
The number of colourings of a polygon such that the multiplicities of a colour are given by a partition.
| Object | Value |
|---|---|
[3] | 1 |
[4] | 1 |
[5] | 1 |
[6] | 1 |
[7] | 1 |
[8] | 1 |
[9] | 1 |
[10] | 1 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001603 has the rest.