Quotients of M-convex sets and M-convex functions

Autor:	Brandenburg, Marie-Charlotte, Loho, Georg, Smith, Ben
Rok vydání:	2024
Předmět:	Mathematics - Combinatorics Mathematics - Algebraic Geometry Mathematics - Optimization and Control 05B35 14T15 52B20 52B40 (Primary) 14M15 90C25 90C27 (Secondary)
Druh dokumentu:	Working Paper
Popis:	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. Comment: 44 pages, 2 figures. Comments welcome
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2403.07751 Zobrazit plný text záznamu View this record from Arxiv