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Antisingletons on SetPartition ​

Elements i with i + 1 in the same block, counting n + 1 as 1.

On SetPartition

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

Live

FindStat St000248

The number of anti-singletons of a set partition.

ObjectValue
{{1,2}}2
{{1,2,3}}3
{{1},{2}}0
{{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/St000248 has the rest.