2020/01/11 by Chuanming Zong, Zong, Chuanming
Computer Science · Mathematics · #Digital Image Processing Techniques #FOS: Mathematics #Limits and Structures in Graph Theory #Metric Geometry (math.MG) #Point processes and geometric inequalities
paper · pdf · doi:10.48550/arxiv.2001.03720
openalex publication_date 2020/01/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In 1933, Borsuk proposed the following problem: Can every bounded set in 𝔼n 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.