The kissing number in four dimensions

• 成果类型: Article
• 署名作者: Musin, Oleg R.
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2008.168.1
• 发表日期: 2008
• 页码: 1-32
• 关键词: minimum distance; unit-sphere; bounds

摘要

The kissing number problem asks for the maximal number k(n) of equal size nonoverlapping spheres in n-dimensional space that call touch another sphere of the same size. This problem in dimension three was the subject of a famous discussion between Isaac Newton and David Gregory in 1694. In three dimensions the problem was finally solved only in 1953 by Schutte and van der Waerden. In this paper we present a solution of a long-standing problem about the kissing number in four dimensions. Namely, the equality k(4) = 24 is proved. The proof is based on a modification of Delsarte's method.