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- W4221164989 abstract "Chromatic symmetric functions are well-studied symmetric functions in algebraic combinatorics that generalize the chromatic polynomial and are related to Hessenberg varieties and diagonal harmonics. Motivated by the Stanley--Stembridge conjecture, we show that the allowable coloring weights for indifference graphs of Dyck paths are the lattice points of a permutahedron $mathcal{P}_lambda$, and we give a formula for the dominant weight $lambda$. Furthermore, we conjecture that such chromatic symmetric functions are Lorentzian, a property introduced by Brand'en and Huh as a bridge between discrete convex analysis and concavity properties in combinatorics, and we prove this conjecture for abelian Dyck paths. We extend our results on the Newton polytope to incomparability graphs of (3+1)-free posets, and we give a number of conjectures and results stemming from our work, including results on the complexity of computing the coefficients and relations with the $zeta$ map from diagonal harmonics." @default.
- W4221164989 created "2022-04-03" @default.
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- W4221164989 date "2022-01-18" @default.
- W4221164989 modified "2023-10-05" @default.
- W4221164989 title "The Newton polytope and Lorentzian property of chromatic symmetric functions" @default.
- W4221164989 doi "https://doi.org/10.48550/arxiv.2201.07333" @default.
- W4221164989 hasPublicationYear "2022" @default.
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