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Asymmetric function theory

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arxiv 1904.01358 v1 pith:Y6WUO6UF submitted 2019-04-02 math.CO

Oliver Pechenik , Dominic Searles This is my paper · ORCID
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The classical theory of symmetric functions has a central position in algebraic combinatorics, bridging aspects of representation theory, combinatorics, and enumerative geometry. More recently, this theory has been fruitfully extended to the larger ring of quasisymmetric functions, with corresponding applications. Here, we survey recent work extending this theory further to general asymmetric polynomials.

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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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