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SumOfBlockMinima on SetPartition ​

The sum of the smallest elements of the blocks.

On SetPartition

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

Live

FindStat St000230

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

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

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000230 has the rest.