Acta mathematica scientia,Series B ›› 2025, Vol. 45 ›› Issue (1): 72-95.doi: 10.1007/s10473-025-0106-x

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ON GENERALIZED KISSING NUMBERS OF CONVEX BODIES

Yiming Li1, Chuanming Zong2,*   

  1. 1. Center for Applied Mathematics, Tianjin University, Tianjin 300072, China;
    2. Center for Applied Mathematics, Tianjin University, Tianjin 300072, China
  • Received:2024-08-16 Published:2025-02-06
  • Contact: *Chuanming Zong, E-mail,: cmzong@tju.edu.cn
  • About author:Yiming Li, E-mail,: xiaozhuang@tju.edu.cn
  • Supported by:
    National Natural Science Foundation of China (12226006, 11921001) and the Natural Key Research and Development Program of China (2018YFA0704701).

Abstract: In 1694, Gregory and Newton proposed the problem to determine the kissing number of a rigid material ball. This problem and its higher dimensional generalization have been studied by many mathematicians, including Minkowski, van der Waerden, Hadwiger, Swinnerton-Dyer, Watson, Levenshtein, Odlyzko, Sloane and Musin. In this paper, we introduce and study a further generalization of the kissing numbers for convex bodies and obtain some exact results, in particular for balls in dimensions three, four and eight.

Key words: convex body, generalized kissing number, E8 lattice

CLC Number: 

  • 52C17
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