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Noncommutative unicellular LLT polynomials

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arxiv 1907.00077 v3 pith:DFIVSB7Q submitted 2019-06-28 math.CO

Jean-Christophe Novelli , Jean-Yves Thibon This is my paper · ORCID
classification math.CO
keywords polynomialsnoncommutativeunicellularalgebrascertainchromaticcombinatorialextension
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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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  1. Chromatic nonsymmetric polynomials of Dyck graphs are slide-positive

    math.CO 2019-08 conditional novelty 6.0 of 10

    Chromatic nonsymmetric polynomials of Dyck graphs are slide-positive, and their backstable limit recovers the known fundamental-basis expansion of chromatic quasisymmetric functions.

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