On Generalized Kissing Numbers of Convex Bodies (II)
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909454553841664 |
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| author | Li, Yiming Zong, Chuanming |
| author_facet | Li, Yiming Zong, Chuanming |
| contents | In 1694, Gregory and Newton discussed 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. Recently, Li and Zong introduced and studied the generalized kissing numbers of convex bodies. As a continuation of this project, in this paper we obtain the exact generalized kissing numbers $κ_α^*(B^n)$ of the $n$-dimensional balls for $3\le n\le 8$ and $α=2\sqrt{3}-2$. Furthermore, the lattice kissing number of a four-dimensional cross-polytope is determined. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2501_06792 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Generalized Kissing Numbers of Convex Bodies (II) Li, Yiming Zong, Chuanming Metric Geometry Combinatorics 52C17, 11H31 In 1694, Gregory and Newton discussed 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. Recently, Li and Zong introduced and studied the generalized kissing numbers of convex bodies. As a continuation of this project, in this paper we obtain the exact generalized kissing numbers $κ_α^*(B^n)$ of the $n$-dimensional balls for $3\le n\le 8$ and $α=2\sqrt{3}-2$. Furthermore, the lattice kissing number of a four-dimensional cross-polytope is determined. |
| title | On Generalized Kissing Numbers of Convex Bodies (II) |
| topic | Metric Geometry Combinatorics 52C17, 11H31 |
| url | https://arxiv.org/abs/2501.06792 |