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SmallestBlock on SetPartition ​

The size of the smallest block.

On SetPartition

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

Live

FindStat St001075

The minimal size of a block of a set partition.

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

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001075 has the rest.