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Order polynomial

The order polynomial is a polynomial studied in mathematics, in particular in algebraic graph theory and algebraic combinatorics. The order polynomial counts the number of order-preserving maps from a poset to a chain of length n {\displaystyle n} . These order-preserving maps were first introduced by Richard P. Stanley while studying ordered structures…

Art, Connections with other counting polynomials & Reciprocity theorem

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Connections with other counting polynomials

ColoringsGraphAcyclic orientationHasse diagramOrder polytope
10 related topics

Reciprocity theorem

Negative binomial identityChromatic polynomialEhrhart polynomialReciprocity Theorem
4 related topics

Definition

FiniteStrictlyLinear extensions
3 related topics

Examples

Identity mappingAntichain
2 related topics

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Reciprocity theorem

Connections with other counting polynomials

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Order polynomial

Nodes34
Edges33
Triples5
Avg. degree1.94
Density0.058824
Components1

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Order polynomial

Top relations

related to Definition · 4
Order polynomial → Let, Omega, Similarly, The
is a · 1
Order polynomial → polynomial studied in mathematics

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Important terminology

displaystyle polynomial order order-preserving poset maps polytope number omega chain ehrhart counts elements phi circ graph linear mathbb strictly polynomials

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SubjectPredicateObjectConfidenceSrc
Order polynomialis apolynomial studied in mathematics0.90text
Order polynomialrelated to DefinitionLet0.60section
Order polynomialrelated to DefinitionThe0.60section
Order polynomialrelated to DefinitionOmega0.60section
Order polynomialrelated to DefinitionSimilarly0.60section

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