Log-concavity for independent sets of valuated matroids Giansiracusa, Jeffrey Rincón, Felipe Schleis, Victoria Ulirsch, Martin 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. 2024 info:eu-repo/semantics/preprint doc-type:preprint text http://purl.org/coar/resource_type/c_816b https://ris.uni-paderborn.de/record/66306 Giansiracusa J, Rincón F, Schleis V, Ulirsch M. Log-concavity for independent sets of valuated matroids. <i>arXiv:240705808</i>. Published online 2024. eng info:eu-repo/semantics/altIdentifier/arxiv/2407.05808 info:eu-repo/semantics/closedAccess