{"pk":64981,"title":"Tutte polynomials of matroids as universal valuative invariants","subtitle":null,"abstract":"We provide a full classification of all families of matroids that are closed under duality and minors, and for which the Tutte polynomial is a universal valuative invariant. There are four inclusion-wise maximal families, two of which are the class of elementary split matroids and the class of graphic Schubert matroids. As a consequence of our framework, we derive new relations among Tutte polynomials of matroids. For example, we show that the Tutte polynomial of every matroid can be expressed uniquely as an integral combination of Tutte polynomials of graphic Schubert matroids.\n \nMathematics Subject Classifications: 05B35, 05C31, 52B40, 52B45\n \nKeywords: Tutte polynomials, matroids, geometric lattices, matroid polytopes, valuations","language":"en","license":{"name":"Creative Commons Attribution 4.0","short_name":"CC BY 4.0","text":"Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.\n\nNo additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.","url":"https://creativecommons.org/licenses/by/4.0"},"keywords":[{"word":"Tutte polynomials"},{"word":"matroids"},{"word":"geometric lattices"},{"word":"matroid polytopes"},{"word":"valuations"}],"section":"Research Articles","is_remote":true,"remote_url":"https://escholarship.org/uc/item/61x272pg","frozenauthors":[{"first_name":"Luis","middle_name":"","last_name":"Ferroni","name_suffix":"","institution":"School of Mathematics, Institute for Advanced Study, Princeton (NJ), U.S.A.","department":""},{"first_name":"Benjamin","middle_name":"","last_name":"Schröter","name_suffix":"","institution":"Department of Mathematics, KTH Royal Institute of Technology, Stockholm, Sweden","department":""}],"date_submitted":"2025-07-15T16:59:47+02:00","date_accepted":"2025-07-15T16:59:47+02:00","date_published":"2025-07-15T09:00:00+02:00","render_galley":null,"galleys":[{"label":"","type":"pdf","path":"https://journalpub.escholarship.org/combinatorial_theory/article/64981/galley/49791/download/"}]}