LeftOpenerSmaller on SetPartition
Pairs of an opener j and a larger element i of a later block.
FindStat's los (left, opener, smaller), the dual major index.
Called as CombinatorialStat(x, "LeftOpenerSmaller"). 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 St000493
The los statistic of a set partition.
| Object | Value |
|---|---|
{{1,2}} | 0 |
{{1,2,3}} | 0 |
{{1},{2}} | 1 |
{{1,2,3,4}} | 0 |
{{1,2},{3}} | 1 |
{{1,3},{2}} | 1 |
{{1},{2,3}} | 2 |
{{1,2,3,4,5}} | 0 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000493 has the rest.