A signed e-expansion of the chromatic quasisymmetric function

2023/11/14 by Foster Tom, Tom, Foster · 1 citation
Mathematics · #Advanced Combinatorial Mathematics

paper · pdf · doi:10.48550/arxiv.2311.08020

Abstract

We prove a new signed elementary symmetric function expansion of the chromatic quasisymmetric function of any natural unit interval graph. We then use a sign-reversing involution to prove a new combinatorial formula for K-chains, which are graphs formed by joining cliques at single vertices. This formula immediately implies e-positivity and e-unimodality for K-chains. We also prove a version of our signed e-expansion for arbitrary graphs.

Cited by

• Towards Upper and Lower Bounds for Chromatic Symmetric Functions in the Elementary Basis

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