IntertwiningNumber on SetPartition
Pairs a < b in different blocks with no element of either block between them.
The block intertwiners of Ehrenborg and Readdy (Juggling and applications to q-analogues), counted over all pairs of blocks.
Called as CombinatorialStat(x, "IntertwiningNumber"). 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 St000490
The intertwining number 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}} | 2 |
{{1},{2,3}} | 1 |
{{1,2,3,4,5}} | 0 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000490 has the rest.