Séminaire Lotharingien de Combinatoire, 95B.34 (2026), 12 pp.
Jon Pål Hamre, Benjamin Schröter, Lorenzo Vecchi and Emil Verkama
Chow Classes of Matroids and Standard Young Tableaux
Abstract.
We study the Chow classes of arbitrary matroids in the Grassmannian. Our main contribution identifies the Poincaré dual of the Chow class of a snake matroid with a specific ribbon Schur function, providing an explicit formula for its coefficients in the Schubert basis as the number of standard Young tableaux of a given shape with a prescribed descent set. This extends to a standard Young tableaux count for the Chow class of any lattice path matroid, and by valuativity to a new expression of this class for any matroid. As consequences, we recover an enumeration by Gessel and Viennot of permutations with fixed descent sets, and provide a formula for the volume of lattice path matroids. Furthermore, we demonstrate the power of our findings by proving that certain Schubert coefficients are positive for all connected paving matroids.
Received: November 15, 2025.
Accepted: February 15, 2026.
Final version: April 1, 2026.
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