Chromatic nonsymmetric polynomials of Dyck graphs are slide-positive
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
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