Morphisms of matroids are combinatorial abstractions of linear maps and graph homomorphisms. We introduce the notion of a 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  for sufficiently small positive parameters.
All Science Journal Classification (ASJC) codes
- Discrete convexity
- Flag matroids
- Lorentzian polynomials
- Multivariate Tutte polynomials