SetPartitions

The partitions of the set into non-empty blocks, a lazy indexed family.

WikipediaPartition of a setMathWorldSetPartitionWikidataQ381060Britannicatopic/partition-of-a-setOEISA000110✓A203646✓A203645✓Wolfram LanguageBellBSageMathSetPartitions(n)SymPymultiset_partitionsmathlib4Finpartition (Finset.univ : Finset (Fin n))Nat.bell

SetPartitions(n)every way to split into disjoint non-empty blocks.

Domain: Collections

Details

A lazy indexed collection; the count is the Bell number — . See BellNumber.
The partitions into exactly blocks number the Stirling numbers of the second kind ; summing over gives . See Stirling.
Each element is the block list; the - glyph draws it from its restricted-growth string.

Enumeration

See also: BellNumber, Stirling, Count, At