A new upper bound for mutually touching infinite cylinders
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918069068103680 |
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| author | Koizumi, Junnosuke |
| author_facet | Koizumi, Junnosuke |
| contents | Let $N$ denote the maximum number of congruent infinite cylinders that can be arranged in $\mathbb{R}^3$ so that every pair of cylinders touches each other. Littlewood posed the question of whether $N=7$, which remains unsolved. In this paper, we prove that $N\leq 18$, improving the previously known upper bound of $24$ established by A. Bezdek. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_19309 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A new upper bound for mutually touching infinite cylinders Koizumi, Junnosuke Metric Geometry Combinatorics 52C17, 52A40, 05D10 Let $N$ denote the maximum number of congruent infinite cylinders that can be arranged in $\mathbb{R}^3$ so that every pair of cylinders touches each other. Littlewood posed the question of whether $N=7$, which remains unsolved. In this paper, we prove that $N\leq 18$, improving the previously known upper bound of $24$ established by A. Bezdek. |
| title | A new upper bound for mutually touching infinite cylinders |
| topic | Metric Geometry Combinatorics 52C17, 52A40, 05D10 |
| url | https://arxiv.org/abs/2506.19309 |