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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

Distribution

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

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.