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BlocksWithEvenMinimum on SetPartition ​

Blocks whose smallest element is even.

On SetPartition

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

Live

FindStat St001153

The number of blocks with even minimum in a set partition.

ObjectValue
{{1}}0
{{1,2}}0
{{1,2,3}}0
{{1},{2}}1
{{1,2,3,4}}0
{{1,2},{3}}0
{{1,3},{2}}1
{{1},{2,3}}1

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001153 has the rest.