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arXiv · 2312.16474

Kromatic quasisymmetric functions

Eric Marberg
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Abstract

We provide a construction for the kromatic symmetric function $\overline{X}_G$ of a graph introduced by Crew, Pechenik, and Spirkl using combinatorial (linearly compact) Hopf algebras. As an application, we show that $\overline{X}_G$ has a positive expansion into multifundamental quasisymmetric functions. We also study two related quasisymmetric $q$-analogues of $\overline{X}_G$, which are $K$-theoretic generalizations of the quasisymmetric chromatic function of Shareshian and Wachs. We classify exactly when one of these analogues is symmetric. For the other, we derive a positive expansion into symmetric Grothendieck functions when $G$ is the incomparability graph of a natural unit interval order.

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Eric Marberg. 2023-12-27. Kromatic quasisymmetric functions. https://doi.org/10.37236/13207

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