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BlockSizeComposition from SetPartition ​

The block sizes of a set partition, its blocks taken in order of their least elements.

SetPartition → IntegerCompositionsurjection

FindStat's Mp00128. Lossy: which elements share a block is forgotten, so it is not a constructor overload.

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

Live

Explore

Each element of SetPartition at a size, and its image, applied in your browser; sizes past 7 are not offered.

Properties

Transport a statistic

Pick a statistic on IntegerComposition. Its distribution over the images of SetPartition at each size is computed, and compared with the 111 statistics on SetPartition: those that share it are the ones the map sends it to, as far as the sizes computed show.

Also from

The same name out of other carriers, each its own implementation: SetComposition.

FindStat Mp00128

to composition

Matched by value: our map agrees with FindStat's image on each of the 278 rows of size at most 6 we can read (0 unread; its table has 1200 rows).

SurjectionGraded mapas FindStat records them, checked by FindStat's contributors.

The integer composition of block sizes of a set partition.
ObjectImage
{{1}}[1]
{{1,2}}[2]
{{1,2,3}}[3]
{{1},{2}}[1,1]

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/Mp00128 has the rest.