Séminaire Lotharingien de Combinatoire, 95B.30 (2026), 12 pp.
Christopher Eur, Alex Fink and Matt Larson
h*-Vectors for Matroids
Abstract.
The Hodge theory of matroids by Adiprasito-Huh-Katz resolved outstanding conjectures in matroid theory by establishing positivity properties for Chow rings of matroids. In algebraic geometry, a notion complementary to the Chow ring is the K-ring of a variety. We establish positivity properties for K-rings of matroids. Our results give a new proof of the nonnegativity of the omega invariant of a matroid, in support of Speyer's f-vector conjecture, and resolve the conjecture of Tohăneanu that higher order Orlik-Terao algebras are Cohen-Macaulay.
Received: November 15, 2025.
Accepted: February 15, 2026.
Final version: April 1, 2026.
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