Chromatic classical symmetric functions
Combinatorics
2018-09-03 v3
Abstract
In this note we classify when a skew Schur function is a positive linear combination of power sum symmetric functions. We then use this to determine precisely when any scalar multiple of a skew Schur function is the chromatic symmetric function of some graph. From here we are able to prove that of the classical bases for symmetric functions only certain scalar multiples of the elementary symmetric functions can be realised as the chromatic symmetric function of some graph, namely a particular union of complete graphs.
Cite
@article{arxiv.1604.03954,
title = {Chromatic classical symmetric functions},
author = {Soojin Cho and Stephanie van Willigenburg},
journal= {arXiv preprint arXiv:1604.03954},
year = {2018}
}
Comments
8 pages, minor adjustments to match final version to appear in J. Comb