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OccurrencesOf12Over3 on SetPartition ​

Occurrences of the pattern 12/3: a < b in one block and c > b in another.

On SetPartition

Called as CombinatorialStat(x, "OccurrencesOf12Over3"). The head's page has its examples.

Live

Distribution

Over SetPartitions at each size, tallied here in your browser; sizes past 10 are not offered.

FindStat St000554

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

ObjectValue
{{1,2}}0
{{1,2,3}}0
{{1},{2}}0
{{1,2,3,4}}0
{{1,2},{3}}1
{{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/St000554 has the rest.