Hyperoctahedral Eulerian idempotents, Hodge decompositions, and signed graph coloring complexes

zbMath1300.05091arXiv1307.7323MaRDI QIDQ405237

Sarah Crown Rundell, Benjamin Braun

Publication date: 4 September 2014

Published in: The Electronic Journal of Combinatorics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1307.7323

zbMATH Keywords

Hodge decompositionchromatic polynomialsigned graphEulerian idempotentcoloring complex

Mathematics Subject Classification ID

Graph polynomials (05C31) Coloring of graphs and hypergraphs (05C15) Chain complexes (category-theoretic aspects), dg categories (18G35) Signed and weighted graphs (05C22)

Cites Work

• 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
• A Hodge decomposition for the complex of injective words.
• Link complexes of subspace arrangements
• The action of \(S_ n\) on the components of the Hodge decomposition of Hochschild homology
• A Hodge-type decomposition for commutative algebra cohomology
• Signed graphs
• Signed graph coloring
• Orthogonal idempotents in the descent algebra of \(B_ n\) and applications
• The Koszul property in affine semigroup rings
• Foulkes characters, Eulerian idempotents, and an amazing matrix
• The topology of the coloring complex
• Coloring complexes and arrangements
• Combinatorics of Coxeter Groups
• A Hodge decomposition interpretation for the coefficients of the chromatic polynomial
• The coloring ideal and coloring complex of a graph
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