At most 10 cylinders mutually touch: a Ramsey-theoretic approach
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914075651342336 |
|---|---|
| author | Dillon, Travis Koizumi, Junnosuke Luo, Sammy |
| author_facet | Dillon, Travis Koizumi, Junnosuke Luo, Sammy |
| contents | Littlewood asked for the maximum number $N$ of congruent infinite cylinders that can be arranged in $\mathbb{R}^3$ so that every pair touches. We improve upon the proof of the second author that $N \leq 18$ to show that $N \leq 10$. Together with the lower bound established by Bozóki, Lee, and Rónyai, this shows that $N \in \{7,8,9,10\}$. Our method is based on linear algebra and Ramsey theory, and makes partial use of computer verification. We also provide a completely computer-free proof that $N \leq 12$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_03924 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | At most 10 cylinders mutually touch: a Ramsey-theoretic approach Dillon, Travis Koizumi, Junnosuke Luo, Sammy Combinatorics Metric Geometry 52C17, 52A40, 05D10 Littlewood asked for the maximum number $N$ of congruent infinite cylinders that can be arranged in $\mathbb{R}^3$ so that every pair touches. We improve upon the proof of the second author that $N \leq 18$ to show that $N \leq 10$. Together with the lower bound established by Bozóki, Lee, and Rónyai, this shows that $N \in \{7,8,9,10\}$. Our method is based on linear algebra and Ramsey theory, and makes partial use of computer verification. We also provide a completely computer-free proof that $N \leq 12$. |
| title | At most 10 cylinders mutually touch: a Ramsey-theoretic approach |
| topic | Combinatorics Metric Geometry 52C17, 52A40, 05D10 |
| url | https://arxiv.org/abs/2510.03924 |