RotationOrbitSize on SetPartition
The number of distinct partitions rotation i -> i + 1 (mod n) makes of this one.
Called as CombinatorialStat(x, "RotationOrbitSize"). The head's page has its examples.
Live
Distribution
Over SetPartitions at each size, tallied here in your browser; sizes past 10 are not offered.
Also on
The same name on other carriers, each its own implementation: IntegerComposition.
FindStat St000163
The size of the orbit of the set partition under rotation.
| Object | Value |
|---|---|
{{1}} | 1 |
{{1,2}} | 1 |
{{1,2,3}} | 1 |
{{1},{2}} | 1 |
{{1,2,3,4}} | 1 |
{{1,2},{3}} | 3 |
{{1,3},{2}} | 3 |
{{1},{2,3}} | 3 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000163 has the rest.