Improved bounds for skew corner-free sets
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866915264337018880 |
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| author | Beker, Adrian |
| author_facet | Beker, Adrian |
| contents | We construct skew corner-free subsets of $[n]^2$ of size $n^2\exp(-O(\sqrt{\log n}))$, thereby improving on recent bounds of the form $Ω(n^{5/4})$ obtained by Pohoata and Zakharov. In the other direction, we prove that any such set has size at most $O(n^2(\log n)^{-c})$ for some absolute constant $c > 0$. This improves on the previously best known upper bound, coming from Shkredov's work on the corners theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_19169 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Improved bounds for skew corner-free sets Beker, Adrian Combinatorics Number Theory We construct skew corner-free subsets of $[n]^2$ of size $n^2\exp(-O(\sqrt{\log n}))$, thereby improving on recent bounds of the form $Ω(n^{5/4})$ obtained by Pohoata and Zakharov. In the other direction, we prove that any such set has size at most $O(n^2(\log n)^{-c})$ for some absolute constant $c > 0$. This improves on the previously best known upper bound, coming from Shkredov's work on the corners theorem. |
| title | Improved bounds for skew corner-free sets |
| topic | Combinatorics Number Theory |
| url | https://arxiv.org/abs/2402.19169 |