@unpublished{66306,
  abstract     = {{Recently, several proofs of the Mason--Welsh conjecture for matroids have been found, which asserts the log-concavity of the sequence that counts independent sets of a given size. In this article we use the theory of Lorentzian polynomials, developed by Brändén and Huh, to prove a generalization of the Mason-Welsh conjecture to the context of valuated matroids. In fact, we provide a log-concavity result in the more general setting of valuated discrete polymatroids, or equivalently, M-convex functions. Our approach is via the construction of a generic extension of a valuated matroid or M-convex function, so that the bases of the extension are related to the independent sets of the original matroid. We also provide a similar log-concavity result for valuated bimatroids, which, we believe, might be of independent interest.}},
  author       = {{Giansiracusa, Jeffrey and Rincón, Felipe and Schleis, Victoria and Ulirsch, Martin}},
  booktitle    = {{arXiv:2407.05808}},
  title        = {{{Log-concavity for independent sets of valuated matroids}}},
  year         = {{2024}},
}