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OverlappingBlockPairs on SetPartition ​

Pairs of blocks A, B with min A < min B < max A < max B.

On SetPartition

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

Live

FindStat St000563

The number of overlapping pairs of blocks of a set partition.

ObjectValue
{{1,2}}0
{{1,2,3}}0
{{1},{2}}0
{{1,2,3,4}}0
{{1,2},{3}}0
{{1,3},{2}}0
{{1},{2,3}}0
{{1,2,3,4,5}}0

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000563 has the rest.