Chromatic nonsymmetric polynomials of Dyck graphs are slide-positive

Vasu Tewari, University of Hawaiʻi at Mānoa
Andrew Timothy Wilson, Kennesaw State University
Philip B. Zhang, Tianjin Normal University


Motivated by the study of Macdonald polynomials, J. Haglund and A. Wilson introduced a nonsymmetric polynomial analogue of the chromatic quasisymmetric function called the chromatic nonsymmetric polynomial of a Dyck graph. We give a positive expansion for this polynomial in the basis of fundamental slide polynomials using recent work of Assaf-Bergeron on flagged (P, p)-partitions. We then derive the known expansion for the chromatic quasisymmetric function of Dyck graphs in terms of Gessel's fundamental basis by taking a backstable limit of our expansion.