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BlocksAndAntisingletons on SetPartition ​

Blocks plus antisingletons.

On SetPartition

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

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FindStat St000250

The number of blocks (St000105) plus the number of antisingletons (St000248) of a set partition.

The number of blocks (St000105) plus the number of antisingletons (St000248) of a set partition.
ObjectValue
{{1,2}}3
{{1,2,3}}4
{{1},{2}}2
{{1,2,3,4}}5
{{1,2},{3}}3
{{1,3},{2}}3
{{1},{2,3}}3
{{1,2,3,4,5}}6

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000250 has the rest.