| Abstract | Motivated by the study of Macdonald polynomials, Haglund and 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,ρ)-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. This work is joint with Vasu Tewari and Andy Wilson. |
