Séminaire Lotharingien de Combinatoire, 93B.72 (2025), 12 pp.
Hsin-Chieh Liao
Equivariant γ-Positivity of Chow Rings and Augmented Chow Rings of Matroids
Abstract.
We prove that the Chow ring and augmented Chow ring of a matroid are equivariant γ-positive under the action of any group of automorphisms of the matroid. This verifies a conjecture of Angarone, Nathanson, and Reiner. Our method gives an explicit interpretation for the coefficients of the equivariant γ-expansion, and extends the author's previous results regarding the positivity of the equivariant Charney-Davis quantity of matroids. Applying the theorems to uniform matroids, we obtain interpretations that extend Shareshian and Wachs' Schur-γ-positivity of the Eulerian and binomial Eulerian quasisymmetric functions, or equivalently, of the cohomologies of the permutahedral and the stellahedral varieties.
Received: November 15, 2024.
Accepted: February 15, 2025.
Final version: April 1, 2025.
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