## Combinatorics Seminar: Logarithmic concavity for morphisms of matroids

Seminar | September 16 | 12:10-1 p.m. | 939 Evans Hall

Christopher Eur, UC Berkeley

Department of Mathematics

Morphisms of matroids are combinatorial abstractions of linear maps and graph homomorphisms. We introduce the notion of basis for morphisms of matroids, and show that its generating function is strongly log-concave. As a consequence, we obtain a generalization of Mason's conjecture on the f-vectors of independent subsets of matroids to arbitrary morphisms of matroids. To establish this, we define multivariate Tutte polynomials of morphisms of matroids, and show that they are Lorentzian (in the sense of Branden and Huh) for sufficiently small positive parameters.

corteel@berkeley.edu