On complete classes of valuated matroids

Husić, Edin, Loho, Georg, Smith, Ben and Végh, László A. ORCID: 0000-0003-1152-200X (2022) On complete classes of valuated matroids. In: Naor, Joseph (Seffi) and Buchbinder, Niv, (eds.) Proceedings of the 2022 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA). Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms. Society for Industrial and Applied Mathematics, 945 - 962. ISBN 9781611977073

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Abstract

We characterize a rich class of valuated matroids, called R-minor valuated matroids that includes the indicator functions of matroids, and is closed under operations such as taking minors, duality, and induction by network. We exhibit a family of valuated matroids that are not R-minor based on sparse paving matroids. Valuated matroids are inherently related to gross substitute valuations in mathematical economics. By the same token we refute the Matroid Based Valuation Conjecture by Ostrovsky and Paes Leme (Theoretical Economics 2015) asserting that every gross substitute valuation arises from weighted matroid rank functions by repeated applications of merge and endowment operations. Our result also has implications in the context of Lorentzian polynomials: it reveals the limitations of known construction operations.

Item Type:	Book Section
Official URL:	https://epubs.siam.org/doi/10.1137/1.9781611977073
Additional Information:	© 2022 The Authors
Divisions:	Mathematics
Subjects:	Q Science > QA Mathematics
Date Deposited:	08 Apr 2022 14:54
Last Modified:	09 Nov 2024 17:24
URI:	http://eprints.lse.ac.uk/id/eprint/114634

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