Hyperoctahedral Eulerian Idempotents, Hodge Decompositions, and Signed Graph Coloring Complexes
Combinatorics
2013-07-30 v1
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 hyperoctahedral Eulerian idempotents.
Keywords
Cite
@article{arxiv.1307.7323,
title = {Hyperoctahedral Eulerian Idempotents, Hodge Decompositions, and Signed Graph Coloring Complexes},
author = {Benjamin Braun and Sarah Crown Rundell},
journal= {arXiv preprint arXiv:1307.7323},
year = {2013}
}