Many unit distances requires many directions
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913778398920704 |
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| author | Currier, Gabriel Solymosi, József |
| author_facet | Currier, Gabriel Solymosi, József |
| contents | In this note, we show that in planar pointsets determining many unit distances, these unit distances must span many directions. Specifically, we show that a set of $n$ points can determine only $o(n^{4/3})$ unit distances from a set of at most $O(n^{1/3})$ directions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_04208 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Many unit distances requires many directions Currier, Gabriel Solymosi, József Combinatorics 52C10, 52C30, 05D99 In this note, we show that in planar pointsets determining many unit distances, these unit distances must span many directions. Specifically, we show that a set of $n$ points can determine only $o(n^{4/3})$ unit distances from a set of at most $O(n^{1/3})$ directions. |
| title | Many unit distances requires many directions |
| topic | Combinatorics 52C10, 52C30, 05D99 |
| url | https://arxiv.org/abs/2504.04208 |