Geodesic
Kromatic quasisymmetric functions
The electronic journal of combinatorics, Tome 32 (2025) no. 1
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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.
DOI : 10.37236/13207
Classification : 05E05, 05C15, 16T30, 11B68
Mots-clés : Eulerian polynomials, \(e\)-positivity, unimodality, Hessenberg varieties 
@article{10_37236_13207,
     author = {Eric Marberg},
     title = {Kromatic quasisymmetric functions},
     journal = {The electronic journal of combinatorics},
     year = {2025},
     volume = {32},
     number = {1},
     doi = {10.37236/13207},
     zbl = {8005218},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/13207/}
}
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Eric Marberg. Kromatic quasisymmetric functions. The electronic journal of combinatorics, Tome 32 (2025) no. 1. doi: 10.37236/13207

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