An analogue of chromatic bases and p-positivity of skew Schur Q-functions

Abstract

We investigate chromatic symmetric functions in relation to the algebra Γ of symmetric functions generated by Schur Q-functions. We construct natural bases of Γ in terms of chromatic symmetric functions. We also consider the p-positivity of skew Schur Q-functions and find a class of p-positive ribbon Schur Q-functions, making a conjecture that they are only p-positive Schur Q-functions. We include many concrete computational results that support our conjecture.