Year: 2025
Type: article
Abstract: We investigate the problem of when a chromatic quasisymmetric function (CQF) X G ( x ; q ) of a graph G is in fact symmetric. We first prove the remarkable fact that if a product of two quasisymmetric functions f and g in countably infinitely many variables is symmetric, then in fact f and g must be symmetric. This allows the problem to be reduced to the case of connected graphs. We then show that any labeled graph having more than one source or sink has a nonsymmetric CQF. As a corollary, we find that all trees other than a directed path have a nonsymmetric CQF. We also show that a family of graphs we call “mixed mountain graphs” always have symmetric CQF.
Source: Algebraic Combinatorics
DOI: 10.5802/alco.448
Authors: Maria Gillespie, Joseph Pappe, Kyle Salois
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
Funder: National Science Foundation
OpenAlex ID: W4415736146