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SmallestCloser on SetPartition ​

The smallest of the blocks' largest elements.

On SetPartition

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

Live

FindStat St000971

The smallest closer of a set partition.

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

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000971 has the rest.