DimensionIndex on SetPartition
The sum over blocks of largest minus smallest element, plus one.
Called as CombinatorialStat(x, "DimensionIndex"). 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 St000229
Sum of the difference between the maximal and the minimal elements of the blocks plus the number of blocks of a set partition.
| Object | Value |
|---|---|
{{1}} | 1 |
{{1,2}} | 2 |
{{1,2,3}} | 3 |
{{1},{2}} | 2 |
{{1,2,3,4}} | 4 |
{{1,2},{3}} | 3 |
{{1,3},{2}} | 4 |
{{1},{2,3}} | 3 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000229 has the rest.