DiagramCoarsenings

Every partition coarser than a diagram's — $\mathrm{Bell}(k)$ of them, for a diagram with $k$ blocks.

DiagramCoarsenings(d)every partition coarser than this one

Typed signatures

Type	Package	Applies
(number) -> list	diagram	always

Domain: Diagram algebras

Examples

Basic #

$\mathrm{Bell}(1)=1$

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

$\mathrm{Bell}(2)=2$

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

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Examples	2

See also: Diagram, OrbitDiagram, InOrbitBasis