{"pk":65044,"title":"Quotients of M-convex sets and M-convex functions","subtitle":null,"abstract":"We unify the study of quotients of matroids, polymatroids, valuated matroids and strong maps of submodular functions in the framework of Murota's discrete convex analysis. As a main result, we compile a list of ten equivalent characterizations of quotients for M-convex sets, generalizing existing formulations for (poly)matroids and submodular functions. We also initiate the study of quotients of M-convex functions, constructing a hierarchy of four separate characterizations. Our investigations yield new insights into the fundamental operation of induction, as well as the structure of linking sets and linking functions, which are generalizations of linking systems and bimatroids.\n \nMathematics Subject Classifications: 05B35, 14T15, 52B20, 52B40, 14M15, 90C25, 90C27\n \nKeywords: Discrete convex functions, flag matroids, discrete convex analysis, matroid theory, matroid quotients, polymatroids","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":"Discrete convex functions"},{"word":"flag matroids"},{"word":"discrete convex analysis"},{"word":"matroid theory"},{"word":"matroid quotients"},{"word":"polymatroids"}],"section":"Research Articles","is_remote":true,"remote_url":"https://escholarship.org/uc/item/9p44h18d","frozenauthors":[{"first_name":"Marie-Charlotte","middle_name":"","last_name":"Brandenburg","name_suffix":"","institution":"Ruhr-Universität Bochum, Bochum, Germany","department":""},{"first_name":"Georg","middle_name":"","last_name":"Loho","name_suffix":"","institution":"University of Twente, Enschede, The Netherlands & Freie Universität Berlin, Berlin, Germany","department":""},{"first_name":"Ben","middle_name":"","last_name":"Smith","name_suffix":"","institution":"Lancaster University, Lancaster, U.K.","department":""}],"date_submitted":"2026-04-20T19:50:28Z","date_accepted":"2026-04-20T19:50:28Z","date_published":"2026-04-20T07:00:00Z","render_galley":null,"galleys":[{"label":"","type":"pdf","path":"https://journalpub.escholarship.org/combinatorial_theory/article/65044/galley/49854/download/"}]}