On the Threshold for Szemerédi's Theorem with Random Differences
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 improves the previous best bounds of $N^{1-\frac{1}{\lceil k/2 \rceil} + o(1)}$ for all odd $k$.
Authors
- Davi Castro-Silva (ORCID: https://orcid.org/0000-0002-7101-5758)
- Jop Briët
Institutions
- Centrum Wiskunde & Informatica (NL)
- QuSoft (NL)
- College of Western Idaho (US)
Publication Details
- Journal
- The Electronic Journal of Combinatorics
- Published
- 2024-10-03
- DOI
- https://doi.org/10.37236/12415
- Primary Topic
- Mathematical Dynamics and Fractals
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Nederlandse Organisatie voor Wetenschappelijk Onderzoek