MaximalNestingCount on PerfectMatching
The most pairs that nest one pair: the largest number of pairs (a, b) with a < c and d < b, over the pairs (c, d).
FindStat's St001046.
Called as CombinatorialStat(x, "MaximalNestingCount"). The head's page has its examples.
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FindStat St001046
The maximal number of arcs nesting a given arc of a perfect matching.
| Object | Value |
|---|---|
[(1,2)] | 0 |
[(1,2),(3,4)] | 0 |
[(1,3),(2,4)] | 0 |
[(1,4),(2,3)] | 1 |
[(1,2),(3,4),(5,6)] | 0 |
[(1,2),(3,5),(4,6)] | 0 |
[(1,2),(3,6),(4,5)] | 1 |
[(1,3),(2,4),(5,6)] | 0 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001046 has the rest.