论文标题
Borsuk猜想的计算机程序
A Computer Program for Borsuk's Conjecture
论文作者
论文摘要
1933年，Borsuk提出了以下问题：可以将$ \ Mathbb {e}^n $中的每个有限设置分为较小直径的$ n+1 $子集吗？许多作者已经研究了这个问题，并且发现了许多部分结果。特别是，卡恩（Kahn）和卡莱（Kalai）的反例在1993年使数学社区感到惊讶。但是，问题仍然远离完全解决。本文对相关主题进行了广泛的评论，并基于新的重新进行了重新制定，介绍了一个计算机证明程序来处理这个众所周知的问题。
In 1933, Borsuk proposed the following problem: Can every bounded set in $\mathbb{E}^n$ be divided into $n+1$ subsets of smaller diameters? This problem has been studied by many authors, and a lot of partial results have been discovered. In particular, Kahn and Kalai's counterexamples surprised the mathematical community in 1993. Nevertheless, the problem is still far away from being completely resolved. This paper presents a broad review on related subjects and, based on a novel reformulation, introduces a computer proof program to deal with this well-known problem.
