Chromatic Symmetric Functions of Hypertrees

2015/06/27 by Taylor, Jair
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1506.08262

Abstract

The chromatic symmetric function X_H of a hypergraph H is the generating function for all colorings of H so that no edge is monochromatic. When H is an ordinary graph, it is known that X_H is positive in the fundamental quasisymmetric functions F_S, but this is not the case for general hypergraphs. We exhibit a class of hypergraphs H --- hypertrees with prime-sized edges --- for which X_H is F-positive, and give an explicit combinatorial interpretation for the F-coefficients of X_H.

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