IncidenceAlgebra

The incidence algebra of a finite poset — basis PosetInterval, product composition of intervals, invertible zeta function whose inverse is MoebiusFunction.

IncidenceAlgebra(poset)the algebra of intervals of the poset

Typed signatures

Type	Package	Applies
(expression<BooleanLattice> | expression<Chain> | expression<DivisorLattice>) -> incidence_algebra	incidence	always

Domain: Incidence algebras

Examples

Basic #

$\binom{5}{2}$ intervals

live ↗

In$\mathrm{AlgebraDimension}(\mathrm{IncidenceAlgebra}(\mathrm{Chain}(4)))$Out$10$

$3^3$ intervals

live ↗

In$\mathrm{AlgebraDimension}(\mathrm{IncidenceAlgebra}(\mathrm{BooleanLattice}(3)))$Out$27$

About

Examples	2

See also: PosetInterval, MoebiusFunction, PosetZeta