A note on the no-$(d+2)$-on-a-sphere problem
| Autor: | Suk, Andrew, White, Ethan Patrick |
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| Rok vydání: | 2024 |
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| Druh dokumentu: | Working Paper |
| Popis: | 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 $\Omega(n^{\frac{1}{d-1}})$ due to Thiele from 1995. Comment: 9 pages |
| Databáze: | arXiv |
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