Chromatic bases for symmetric functions

Abstract

In this note we obtain numerous new bases for the algebra of symmetric functions whose generators are chromatic symmetric functions. More precisely, if $\{G_k{\}}_{k\ge 1}$ is a set of connected graphs such that $G_k$ has $k$ vertices for each $k$, then the set of all chromatic symmetric functions $\{X_{G_k}{\}}_{k\ge 1}$ generates the algebra of symmetric functions. We also obtain explicit expressions for the generators arising from complete graphs, star graphs, path graphs and cycle graphs.

6 pages, final version that appeared in Electron. J. Combin. with the missing term in Theorem 8 Part 4 added. The authors would like to thank Samantha Dahlberg for alerting them to this omission

References in corpus (1)

• A modular relation for the chromatic symmetric functions of (3+1)-free posets