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OccurrencesOf13Over2Openers1Closers2 on SetPartition ​

Occurrences of the pattern 13/2 with 1 the least element of its block and 2 the greatest element of its block.

On SetPartition

Called as CombinatorialStat(x, "OccurrencesOf13Over2Openers1Closers2"). The head's page has its examples.

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Distribution

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

FindStat St000581

The number of occurrences of the pattern {{1,3},{2}} such that 1 is minimal, 2 is maximal.

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

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000581 has the rest.