BlockSizeComposition

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

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

Typed signatures

Type	Package	Applies
`((set_composition) -> composition) & ((set_partition) -> composition)`	`combinatorics`	always

Domain: Combinatorial maps

Details

Takes a SetPartition and returns a IntegerComposition — a typed map, so a wrong carrier is a type error rather than a wrong answer.
FindStat's Mp00128. Lossy: which elements share a block is forgotten, so it is not a constructor overload.
Also takes a SetComposition, returning a IntegerComposition: The block sizes of a set composition, its blocks taken in order.
FindStat's Mp00287. Lossy: which elements share a block is forgotten.

Examples

Basic #

the set partition $\{1,3\} \mid \{2\} \mid \{4\}$

\mathrm{BlockSizeComposition}({\operatorname{SetPartition}}([[1, 3], [2], [4]]))

Out

{\operatorname{IntegerComposition}}([2, 1, 1])

the set composition $\{2,4\} \mid \{1\} \mid \{3\}$

\mathrm{BlockSizeComposition}({\operatorname{SetComposition}}([[2, 4], [1], [3]]))

Out

{\operatorname{IntegerComposition}}([2, 1, 1])

About

Examples	2
Crosswalk	FindStat ×2