CrossingsPlusTwiceNestings on PerfectMatching
The crossings plus twice the nestings.
FindStat's St000043. For a pair opening before another, the other opens inside it when it crosses or nests, and closes inside it when it nests, so 1 for the first and 2 for both.
Called as CombinatorialStat(x, "CrossingsPlusTwiceNestings"). The head's page has its examples.
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FindStat St000043
The number of crossings plus two-nestings of a perfect matching.
| Object | Value |
|---|---|
[(1,2)] | 0 |
[(1,2),(3,4)] | 0 |
[(1,3),(2,4)] | 1 |
[(1,4),(2,3)] | 2 |
[(1,2),(3,4),(5,6)] | 0 |
[(1,2),(3,5),(4,6)] | 1 |
[(1,2),(3,6),(4,5)] | 2 |
[(1,3),(2,4),(5,6)] | 1 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000043 has the rest.