CrossingNumber on SetPartition
The largest number of arcs that mutually cross.
FindStat's St000253. A set of arcs mutually crosses when all start before any ends; the longest such chain is found at each point between starts and ends.
Called as CombinatorialStat(x, "CrossingNumber"). The head's page has its examples.
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Distribution
Over SetPartitions at each size, tallied here in your browser; sizes past 10 are not offered.
FindStat St000253
The crossing number of a set partition.
| Object | Value |
|---|---|
{{1,2}} | 1 |
{{1,2,3}} | 1 |
{{1},{2}} | 0 |
{{1,2,3,4}} | 1 |
{{1,2},{3}} | 1 |
{{1,3},{2}} | 1 |
{{1},{2,3}} | 1 |
{{1,2,3,4,5}} | 1 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000253 has the rest.