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 [BH19] for sufficiently small positive parameters.

中文翻译：

---

拟阵的态射的对数凹度

拟阵的态射是线性映射和图同态的组合抽象。我们引入拟阵态射基的概念，并证明其生成函数是强对数凹函数。因此，我们获得了对拟阵独立子集的 $f$ 向量的梅森猜想到拟阵的任意态射的推广。为了建立这一点，我们定义了拟阵态射的多元 Tutte 多项式，并表明它们是 [BH19] 意义上的洛伦兹，对于足够小的正参数。