RightOpenerSmaller on SetPartition
Pairs of an opener j and a larger element i of an earlier block.
FindStat's ros (right, opener, smaller): an inversion of the set partition in Steingrímsson's sense.
Called as CombinatorialStat(x, "RightOpenerSmaller"). 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 St000491
The number of inversions of a set partition.
| Object | Value |
|---|---|
{{1,2}} | 0 |
{{1,2,3}} | 0 |
{{1},{2}} | 0 |
{{1,2,3,4}} | 0 |
{{1,2},{3}} | 0 |
{{1,3},{2}} | 1 |
{{1},{2,3}} | 0 |
{{1,2,3,4,5}} | 0 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000491 has the rest.