UnsplittableFactorCount on SetPartition
The number of unsplittable factors of the set partition under the split product.
FindStat's St000823. The split product of set partitions of m and n glues the i-th block of the first to the i-th block of the second, shifted by m.
Called as CombinatorialStat(x, "UnsplittableFactorCount"). The head's page has its examples.
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Distribution
Over SetPartitions at each size, tallied here in your browser; sizes past 10 are not offered.
FindStat St000823
The number of unsplittable factors of the set partition.
| Object | Value |
|---|---|
{{1,2}} | 2 |
{{1,2,3}} | 3 |
{{1},{2}} | 1 |
{{1,2,3,4}} | 4 |
{{1,2},{3}} | 2 |
{{1,3},{2}} | 2 |
{{1},{2,3}} | 1 |
{{1,2,3,4,5}} | 5 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000823 has the rest.