关于集合的多重Borsuk数
On the multiple Borsuk numbers of sets
摘要：
n维欧氏空间中直径d >0的集合S的Borsuk数是m的最小值，使得S可以被划分为m个直径小于d的集合。我们的目的是推广这个概念如下：这样一个集合S的k重Borsuk数是m的最小值，使得存在S的k重覆盖，m个集合的直径小于d。本文刻画了欧氏平面上集合的k重Borsuk数，给出了中心对称集、光滑体和常宽凸体的k重Borsuk数的界，并对欧氏空间中的有限点集进行了检验.
英文摘要：
The Borsuk number of a set S of diameter d >0 in Euclidean n-space is the smallest value of m such that S can be partitioned into m sets of diameters less than d. Our aim is to generalize this notion in the following way: The k-fold Borsuk number of such a set S is the smallest value of m such that there is a k-fold cover of S with m sets of diameters less than d. In this paper we characterize the k-fold Borsuk numbers of sets in the Euclidean plane, give bounds for those of centrally symmetric sets, smooth bodies and convex bodies of constant width, and examine them for finite point sets in the Euclidean 3-space.
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。
