Chromatic nonsymmetric polynomials of Dyck graphs are slide-positive

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