---
res:
  bibo_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.@eng
  bibo_authorlist:
  - foaf_Person:
      foaf_givenName: Jeffrey
      foaf_name: Giansiracusa, Jeffrey
      foaf_surname: Giansiracusa
  - foaf_Person:
      foaf_givenName: Felipe
      foaf_name: Rincón, Felipe
      foaf_surname: Rincón
  - foaf_Person:
      foaf_givenName: Victoria
      foaf_name: Schleis, Victoria
      foaf_surname: Schleis
  - foaf_Person:
      foaf_givenName: Martin
      foaf_name: Ulirsch, Martin
      foaf_surname: Ulirsch
      foaf_workInfoHomepage: http://www.librecat.org/personId=114697
  dct_date: 2024^xs_gYear
  dct_language: eng
  dct_title: Log-concavity for independent sets of valuated matroids@
...