The prime grid contains arbitrarily large empty polygons
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909392532668416 |
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| author | Dillon, Travis |
| author_facet | Dillon, Travis |
| contents | This paper proves a 2017 conjecture of De Loera, La Haye, Oliveros, and Roldán-Pensado that the "prime grid" $\big\{(p,q) \in \mathbb{Z}^2 : \text{$p$ and $q$ are prime}\big\} \subseteq \mathbb{R}^2$ contains empty polygons with arbitrarily many vertices. This implies that no Helly-type theorem is true for the prime grid. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_10549 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The prime grid contains arbitrarily large empty polygons Dillon, Travis Combinatorics Metric Geometry Number Theory This paper proves a 2017 conjecture of De Loera, La Haye, Oliveros, and Roldán-Pensado that the "prime grid" $\big\{(p,q) \in \mathbb{Z}^2 : \text{$p$ and $q$ are prime}\big\} \subseteq \mathbb{R}^2$ contains empty polygons with arbitrarily many vertices. This implies that no Helly-type theorem is true for the prime grid. |
| title | The prime grid contains arbitrarily large empty polygons |
| topic | Combinatorics Metric Geometry Number Theory |
| url | https://arxiv.org/abs/2411.10549 |