A note on the no-$(d+2)$-on-a-sphere problem
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866915047620476928 |
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| author | Suk, Andrew White, Ethan Patrick |
| author_facet | Suk, Andrew White, Ethan Patrick |
| contents | For fixed $d\geq 3$, we construct subsets of the $d$-dimensional lattice cube $[n]^d$ of size $n^{\frac{3}{d + 1} - o(1)}$ with no $d+2$ points on a sphere or a hyperplane. This improves the previously best known bound of $Ω(n^{\frac{1}{d-1}})$ due to Thiele from 1995. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_02866 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A note on the no-$(d+2)$-on-a-sphere problem Suk, Andrew White, Ethan Patrick Combinatorics Discrete Mathematics 52C35, 52C10, 05D40 For fixed $d\geq 3$, we construct subsets of the $d$-dimensional lattice cube $[n]^d$ of size $n^{\frac{3}{d + 1} - o(1)}$ with no $d+2$ points on a sphere or a hyperplane. This improves the previously best known bound of $Ω(n^{\frac{1}{d-1}})$ due to Thiele from 1995. |
| title | A note on the no-$(d+2)$-on-a-sphere problem |
| topic | Combinatorics Discrete Mathematics 52C35, 52C10, 05D40 |
| url | https://arxiv.org/abs/2412.02866 |