M-凸集与M-凸函数的商
Quotients of M-convex sets and M-convex functions
AI总结：
该研究在离散凸分析框架下统一研究拟阵等对象的商与子模函数强映射，给出M-凸集商的十种等价刻画，首次研究M-凸函数的商并构建四类刻画层级，深化了对归纳运算及连接集、函数结构的理解。
摘要：
我们在Murota的离散凸分析框架下，统一了对拟阵、多拟阵、赋值拟阵的商以及子模函数强映射的研究。作为主要结果，我们整理出M-凸集商的十种等价刻画，推广了现有针对（多）拟阵和子模函数的表述。我们还首次开展了M-凸函数商的研究，构建了包含四种不同刻画的层级结构。我们的研究为归纳这一基本运算，以及作为连接系统和双拟阵推广的连接集、连接函数的结构提供了新的见解。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
