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PropagatingNumber on PerfectMatching ​

Pairs with one point among the first n and the other among the last n, for a matching of 2n points.

On PerfectMatching

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

Live

FindStat St000819

The propagating number of a perfect matching.

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

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000819 has the rest.