Soojin Cho, Stephanie van Willigenburg
Published 2016-04-13Version 1
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 a skew Schur function is the chromatic symmetric function of some graph. As a consequence we prove that of the classical bases for symmetric functions only the elementary symmetric functions can be realised as the chromatic symmetric function of some graph, namely a particular union of complete graphs.
Resolving Stanley's e-positivity of claw-contractible-free graphs
Positivity of chromatic symmetric functions associated with Hessenberg functions of bounce number 3
Proper $q$-caterpillars are distinguished by their Chromatic Symmetric Functions
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