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LargestOpener on SetPartition ​

The largest of the blocks' smallest elements.

On SetPartition

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

Live

FindStat St000839

The largest opener of a set partition.

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

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000839 has the rest.