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SameBlockTriples on SetPartition ​

Triples of elements in one block.

On SetPartition

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

Live

FindStat St000561

The number of occurrences of the pattern {{1,2,3}} in a set partition.

ObjectValue
{{1,2}}0
{{1,2,3}}1
{{1},{2}}0
{{1,2,3,4}}4
{{1,2},{3}}0
{{1,3},{2}}0
{{1},{2,3}}0
{{1,2,3,4,5}}10

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000561 has the rest.