Séminaire Lotharingien de Combinatoire, 89B.23 (2023), 12 pp.
Andrew Berget, Christopher Eur, Hunter Spink and
Dennis Tseng
Tautological Classes of Matroids
Abstract.
We introduce certain classes on permutohedral varieties which we call "tautological classes of matroids" as a new framework for studying matroids. Using this framework, we unify and extend many recent developments in matroid theory arising from its interaction with algebraic geometry. We achieve this by establishing a cohomological description and a log-concavity property for a 4-variable transformation of the Tutte polynomial, and by establishing an exceptional Hirzebruch-Riemann-Roch formula for permutohedral varieties that bridges K-theory and cohomology theory.
Received: November 15, 2022.
Accepted: February 20, 2023.
Final version: April 1, 2023.
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