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.
The Soojin Cho and the JiSun Huh were supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2015R1D1A1A01057476). The Sun-Young Nam was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-R1D1A1B03030945 and NRF-2019R1I1A1A01062658)The authors are grateful to the referees for their careful reading and helpful comments. The authors would like to thank Stephanie van Willigenburg for helpful conversations, Sogang University and Korea Institute for Advanced Study where some of the research took place.
