ConjugateComposition

The conjugate (transpose) composition $\alpha^{*}$: the transpose of the ribbon's skew shape, gotten by complementing the descent set inside $\{1,\ldots,n-1\}$ and reversing.

WikipediaQuasisymmetric function↗Quasisymmetric function↗WikidataQ7269535↗

ConjugateComposition(composition)$\alpha^{*}$, the transpose of composition

Typed signatures

Type	Package	Applies
(list<integer>) -> list	hopf	always

Domain: Hopf algebras

Examples

Basic #

The transpose of a single row is a column

live ↗

In$\mathrm{ConjugateComposition}(\bigl\lbrack3\bigr\rbrack)$Out$\bigl\lbrack1, 1, 1\bigr\rbrack$

live ↗

In$\mathrm{ConjugateComposition}(\bigl\lbrack2, 1, 1\bigr\rbrack)$Out$\bigl\lbrack3, 1\bigr\rbrack$

About

Examples	2
Crosswalk	Wikipedia ×2Wikidata

See also: NSymH, Antipode