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arXiv · 2304.03234

On the threshold for Szemerédi's theorem with random differences

Jop Briët·Davi Castro-Silva
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Abstract

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 $k$.

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Jop Briët, Davi Castro-Silva. 2024-11-05. On the threshold for Szemerédi's theorem with random differences. https://doi.org/10.37236/12415

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