Chromatic nonsymmetric polynomials of Dyck graphs are slide-positive

Authors

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

Department

Mathematics

Document Type

Article

Publication Date

1-1-2022

Abstract

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.

Journal Title

Proceedings of the American Mathematical Society

Journal ISSN

00029939

Volume

150

Issue

5

First Page

1873

Last Page

1888

Digital Object Identifier (DOI)

10.1090/proc/15664