ClosersBelowLargestOpener on PerfectMatching

The pairs whose larger point is below the largest opener, the larger point of the pair opening last.

On PerfectMatching

FindStat's St000840. Every other opener is below the largest, so the closers below it number the largest opener less the pairs.

Called as CombinatorialStat(x, "ClosersBelowLargestOpener"). The head's page has its examples.

Live

FindStat St000840

The number of closers smaller than the largest opener in a perfect matching.

Object	Value
[(1,2)]	0
[(1,2),(3,4)]	1
[(1,3),(2,4)]	0
[(1,4),(2,3)]	0
[(1,2),(3,4),(5,6)]	2
[(1,2),(3,5),(4,6)]	1
[(1,2),(3,6),(4,5)]	1
[(1,3),(2,4),(5,6)]	2

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000840 has the rest.