TransposeComposition

The conjugate composition: its ribbon shape transposed, the complement of the reverse.

FindStatMp00041via IntegerComposition↗

TransposeComposition(IntegerComposition)The conjugate composition: its ribbon shape transposed, the complement of the reverse.

Typed signatures

Type	Package	Applies
(composition) -> composition	combinatorics	always

Domain: Combinatorial maps

Details

• Takes a IntegerComposition and returns a IntegerComposition — a typed map, so a wrong carrier is a type error rather than a wrong answer.
• Defined as a COMPOSITION, applied right to left: Complement after Reverse. Each step goes through its own declared head, so every intermediate value is a properly constructed carrier.
• FindStat's "conjugate" on compositions, named for TransposePartition and TransposeTableau: Conjugate is already the complex conjugate. hopf's ConjugateComposition is the same operation on a plain list of parts.

Examples

Basic #

the composition $2 + 1 + 3$

live ↗

In$\mathrm{TransposeComposition}({\operatorname{IntegerComposition}}([2, 1, 3]))$Out${\operatorname{IntegerComposition}}([1, 1, 3, 1])$

About

Examples	1
Crosswalk	FindStat

See also: Complement, Reverse