论文标题
M $ {}^\ Natural $ -convex函数的压缩 - 标志Matroids and Valued permutohedra
Compression of M${}^\natural$-convex Functions -- Flag Matroids and Valuated Permutohedra
论文作者
论文摘要
Murota（1998）和Murota和Shioura（1999）引入了M-Convex功能和M $ {}^\ Natural $ -convex函数作为离散凸功能的概念，这些函数是由于着装和Wenzel（1992）而导致的有价值的矩阵的概括。在本文中，我们考虑了由M $ {}^\ Natural $ -Convex函数的部分卷积定义的新操作，该函数将给定的M $ {}^\ natural $ -convex函数转换为M-Convex函数，我们称之为M $ {}^}^\ natural $ -convex函数。对于有价值的广义型矩阵（特殊的M $ {}^\ Natural $ -Convex函数），压缩功能可引起有价值的置换式螺旋体，并分解有价值的通用型曲Matroid到Flag-Matroid Strips中，每条都与诱导的渗透率的最大线性域相对应。我们通过对MUROTA的离散凸分析来检查Flag-电语条的结构和诱导的置换式体系的细节。
Murota (1998) and Murota and Shioura (1999) introduced concepts of M-convex function and M${}^\natural$-convex function as discrete convex functions, which are generalizations of valuated matroids due to Dress and Wenzel (1992). In the present paper we consider a new operation defined by a convolution of sections of an M${}^\natural$-convex function that transforms the given M${}^\natural$-convex function to an M-convex function, which we call a compression of an M${}^\natural$-convex function. For the class of valuated generalized matroids, which are special M${}^\natural$-convex functions, the compression induces a valuated permutohedron together with a decomposition of the valuated generalized matroid into flag-matroid strips, each corresponding to a maximal linearity domain of the induced valuated permutohedron. We examine the details of the structure of flag-matroid strips and the induced valuated permutohedron by means of discrete convex analysis of Murota.
