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

Benjamin Braun, Sarah Crown Rundell

Research output: Contribution to journalArticlepeer-review

Abstract

Phil Hanlon proved that the coefficients of the chromatic polynomial of a graph G are equal (up to sign) to the dimensions of the summands in a Hodge-type decomposition of the top homology of the coloring complex for G. We prove a type B analogue of this result for chromatic polynomials of signed graphs using hyperocta- hedral Eulerian idempotents.

Original languageEnglish
Article numberP2.35
JournalElectronic Journal of Combinatorics
Volume21
Issue number2
DOIs
StatePublished - May 22 2014

Keywords

  • Chromatic polynomial
  • Coloring complex
  • Eulerian idempotent
  • Hodge decomposition
  • Signed graph

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics
  • Applied Mathematics

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