An incomplete attack on the upper bound of the unit distance problem
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2026
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866911717722685440 |
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| author | Senger, Steven |
| author_facet | Senger, Steven |
| contents | This is an incomplete attempt to show that the upper bound of $\lesssim n^\frac{4}{3}$ on the number unit distances determined by a large finite set of $n$ points in the plane is not sharp. The methods also say something about sets of $n$ points and $n$ lines that attain the sharp bound of the Szemerédi-Trotter point-line incidence bound. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_26145 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | An incomplete attack on the upper bound of the unit distance problem Senger, Steven General Mathematics 52C10, 51A20 This is an incomplete attempt to show that the upper bound of $\lesssim n^\frac{4}{3}$ on the number unit distances determined by a large finite set of $n$ points in the plane is not sharp. The methods also say something about sets of $n$ points and $n$ lines that attain the sharp bound of the Szemerédi-Trotter point-line incidence bound. |
| title | An incomplete attack on the upper bound of the unit distance problem |
| topic | General Mathematics 52C10, 51A20 |
| url | https://arxiv.org/abs/2605.26145 |