SetPartitionRank on SetPartition
The number of elements minus the number of blocks.
Called as CombinatorialStat(x, "SetPartitionRank"). 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.
FindStat St000211
The rank of the set partition.
| Object | Value |
|---|---|
{{1}} | 0 |
{{1,2}} | 1 |
{{1,2,3}} | 2 |
{{1},{2}} | 0 |
{{1,2,3,4}} | 3 |
{{1,2},{3}} | 1 |
{{1,3},{2}} | 1 |
{{1},{2,3}} | 1 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000211 has the rest.