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SumOfBlockMaxima on SetPartition ​

The sum of the largest elements of the blocks.

On SetPartition

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

Live

FindStat St000231

Sum of the maximal elements of the blocks of a set partition.

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

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000231 has the rest.