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FlattenedMajorIndex on SetPartition ​

The major index of the permutation listing the blocks in order, each ascending.

On SetPartition

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

Live

Distribution

Over SetPartitions at each size, tallied here in your browser; sizes past 10 are not offered.

FindStat St000748

The major index of the permutation obtained by flattening the set partition.

ObjectValue
{{1,2}}0
{{1,2,3}}0
{{1},{2}}0
{{1,2,3,4}}0
{{1,2},{3}}0
{{1,3},{2}}2
{{1},{2,3}}0
{{1,2,3,4,5}}0

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000748 has the rest.