Jon Pål Hamre: Chow classes of matroids

Abstract: We study the class of a matroid in the Chow ring of the Grassmannian. The coefficients appearing when expressing the Chow class in the Schubert basis are conjectured to be nonnegative. However all previous expressions for these Chow classes are too complicated to understand its behavior. We give new combinatorial interpretations of the Chow class of Snake matroids. Both in terms counting certain standard Young tableaux, and as a skew Schur function. Our results easily extends to all lattice path matroids, and together with results by Hampe to arbitrary matroids. We use our results to give simple proofs of known results in the literature. We also confirm the nonnegativity conjecture for certain coefficients of paving matroids.

This is based on joint work with Benjamin Schröter, Lorenzo Vecchi and Emil Verkama.