A Hodge decomposition interpretation for the coefficients of the chromatic polynomial

DOI10.1090/S0002-9939-08-08974-0zbMath1146.05023MaRDI QIDQ3532497

Philip J. Hanlon

Publication date: 28 October 2008

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

chromatic polynomialcoloring complexEulerian idempotentstop homologynumber of acyclic orientationsHodge pieces

Mathematics Subject Classification ID

Coloring of graphs and hypergraphs (05C15) Chain complexes (category-theoretic aspects), dg categories (18G35)

Related Items (6)

Hyperoctahedral Eulerian idempotents, Hodge decompositions, and signed graph coloring complexes ⋮ \(p\)-adic roots of chromatic polynomials ⋮ The coloring complex and cyclic coloring complex of a complete \(k\)-uniform hypergraph ⋮ Hypergraph coloring complexes ⋮ The Hodge structure of the coloring complex of a hypergraph ⋮ Functions of random walks on hyperplane arrangements

Cites Work

• Unnamed Item
• The shuffle bialgebra and the cohomology of commutative algebras
• The action of \(S_ n\) on the components of the Hodge decomposition of Hochschild homology
• The topology of the coloring complex
• A symmetric function generalization of the chromatic polynomial of a graph
• Acyclic orientations of graphs
• Hodge structures on posets
• A logical expansion in mathematics
• The coloring ideal and coloring complex of a graph

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