MaximalRightCrossingCount on PerfectMatching
The most pairs (c, d) with a < c < b < d, over the pairs (a, b): arcs that cross a given arc at its right end.
FindStat's St001047 counts these, though its title says arcs crossing a given arc: its code sweeps the closers and counts the arcs opened inside and still open, which leaves out the arcs crossing at the left end.
Called as CombinatorialStat(x, "MaximalRightCrossingCount"). The head's page has its examples.
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FindStat St001047
The maximal number of arcs crossing a given arc of a perfect matching.
| Object | Value |
|---|---|
[(1,2)] | 0 |
[(1,2),(3,4)] | 0 |
[(1,3),(2,4)] | 1 |
[(1,4),(2,3)] | 0 |
[(1,2),(3,4),(5,6)] | 0 |
[(1,2),(3,5),(4,6)] | 1 |
[(1,2),(3,6),(4,5)] | 0 |
[(1,3),(2,4),(5,6)] | 1 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001047 has the rest.