InDiagramBasis

Rewrite a partition-algebra element in the diagram basis $d_\lambda$, by Möbius inversion over the partition lattice when it arrived in the orbit basis.

InDiagramBasis(x)the element rewritten in the diagram basis

Typed signatures

Type	Package	Applies
(number) -> number	diagram	always

Domain: Diagram algebras

Examples

Basic #

Möbius inversion over the partition lattice

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In$\mathrm{InDiagramBasis}(\mathrm{OrbitDiagram}(\bigl\lbrack\bigl\lbrack1\bigr\rbrack, \bigl\lbrack-1\bigr\rbrack\bigr\rbrack))$Out$\mathrm{Diagram}(\bigl\lbrack\bigl\lbrack1\bigr\rbrack, \bigl\lbrack-1\bigr\rbrack\bigr\rbrack)-\mathrm{Diagram}(\bigl\lbrack\bigl\lbrack1, -1\bigr\rbrack\bigr\rbrack)$

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See also: Diagram, OrbitDiagram, InOrbitBasis