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LargestElementInFirstBlock on SetPartition ​

The largest element of the block containing 1.

On SetPartition

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

Live

FindStat St000505

The biggest entry in the block containing the 1.

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}}3
{{1},{2,3}}1

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000505 has the rest.