{"type":"preprint","date_created":"2026-07-08T06:22:23Z","external_id":{"arxiv":["2407.05808"]},"abstract":[{"text":"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.","lang":"eng"}],"citation":{"ieee":"J. Giansiracusa, F. Rincón, V. Schleis, and M. Ulirsch, “Log-concavity for independent sets of valuated matroids,” <i>arXiv:2407.05808</i>. 2024.","apa":"Giansiracusa, J., Rincón, F., Schleis, V., &#38; Ulirsch, M. (2024). Log-concavity for independent sets of valuated matroids. In <i>arXiv:2407.05808</i>.","chicago":"Giansiracusa, Jeffrey, Felipe Rincón, Victoria Schleis, and Martin Ulirsch. “Log-Concavity for Independent Sets of Valuated Matroids.” <i>ArXiv:2407.05808</i>, 2024.","short":"J. Giansiracusa, F. Rincón, V. Schleis, M. Ulirsch, ArXiv:2407.05808 (2024).","mla":"Giansiracusa, Jeffrey, et al. “Log-Concavity for Independent Sets of Valuated Matroids.” <i>ArXiv:2407.05808</i>, 2024.","bibtex":"@article{Giansiracusa_Rincón_Schleis_Ulirsch_2024, title={Log-concavity for independent sets of valuated matroids}, journal={arXiv:2407.05808}, author={Giansiracusa, Jeffrey and Rincón, Felipe and Schleis, Victoria and Ulirsch, Martin}, year={2024} }","ama":"Giansiracusa J, Rincón F, Schleis V, Ulirsch M. Log-concavity for independent sets of valuated matroids. <i>arXiv:240705808</i>. Published online 2024."},"publication":"arXiv:2407.05808","user_id":"82981","_id":"66306","language":[{"iso":"eng"}],"date_updated":"2026-07-08T06:22:38Z","author":[{"last_name":"Giansiracusa","first_name":"Jeffrey","full_name":"Giansiracusa, Jeffrey"},{"full_name":"Rincón, Felipe","first_name":"Felipe","last_name":"Rincón"},{"last_name":"Schleis","first_name":"Victoria","full_name":"Schleis, Victoria"},{"id":"114697","last_name":"Ulirsch","first_name":"Martin","full_name":"Ulirsch, Martin"}],"status":"public","year":"2024","title":"Log-concavity for independent sets of valuated matroids"}