Tautological classes of matroids

We introduce certain torus-equivariant classes on permutohedral varieties which we call “tautological of matroids” as a new geometric framework for studying matroids. Using this framework, unify and extend many recent developments in matroid theory arising from its interaction with algebraic geometry. achieve by establishing Chow-theoretic description log-concavity property 4-variable transformation the Tutte polynomial, an exceptional Hirzebruch-Riemann-Roch-type formula that translates between $K$ -theory Chow theory.