e-positive partitions for chromatic symmetric functions

2026/06/30 by Noah Kravitz
#math.CO

paper · pdf

Abstract

We show that the partitions that always appear with nonnegative e-coefficients in chromatic symmetric functions of finite graphs are precisely the hook partitions.

Citations

• Chromatic symmetric functions of claw-free graphs are not Schur positive
• A proof of the Stanley--Stembridge conjecture
• Chromatic symmetric functions and change of basis
• Resolving Stanley's e-positivity of claw-contractible-free graphs
• Hook coefficients of chromatic functions

Related

• Hook coefficients of chromatic functions
• The chromatic symmetric function of a graph centred at a vertex
• Classes of graphs with e-positive chromatic symmetric function
• Towards Upper and Lower Bounds for Chromatic Symmetric Functions in the Elementary Basis
• A quantitative way to e-positivity of trees