Chromatic nonsymmetric polynomials of Dyck graphs are slide-positive, and their backstable limit recovers the known fundamental-basis expansion of chromatic quasisymmetric functions.
Noncommutative unicellular LLT polynomials
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abstract
It is known that unicellular LLT polynomials are related to the quasi-symmetric chromatic polynomials of certain graphs by the $(t-1)$-transform of symmetric functions. We investigate the extension of this transformation to various combinatorial Hopf algebras and prove a noncommutative version of this property.
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Chromatic nonsymmetric polynomials of Dyck graphs are slide-positive
Chromatic nonsymmetric polynomials of Dyck graphs are slide-positive, and their backstable limit recovers the known fundamental-basis expansion of chromatic quasisymmetric functions.