On the threshold for Szemerédi's theorem with random differences
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866912104954462208 |
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| author | Briët, Jop Castro-Silva, Davi |
| author_facet | Briët, Jop Castro-Silva, Davi |
| contents | Using recent developments on the theory of locally decodable codes, we prove that the critical size for Szemerédi's theorem with random differences is bounded from above by $N^{1-\frac{2}{k} + o(1)}$ for length-$k$ progressions. This gives polynomial improvements over the previous best bounds for all odd $k$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_03234 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the threshold for Szemerédi's theorem with random differences Briët, Jop Castro-Silva, Davi Combinatorics 11B30, 05D40 Using recent developments on the theory of locally decodable codes, we prove that the critical size for Szemerédi's theorem with random differences is bounded from above by $N^{1-\frac{2}{k} + o(1)}$ for length-$k$ progressions. This gives polynomial improvements over the previous best bounds for all odd $k$. |
| title | On the threshold for Szemerédi's theorem with random differences |
| topic | Combinatorics 11B30, 05D40 |
| url | https://arxiv.org/abs/2304.03234 |