{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/diagonal-ramsey-via-effective-quasirandomness","title":"Diagonal Ramsey via effective quasirandomness","arxiv_id":"2005.09251","date":"2020-05-19","proceeding":null,"authors":["Ashwin Sah"],"abstract":"We improve the upper bound for diagonal Ramsey numbers to \\[R(k+1,k+1)\\le\\exp(-c(\\log k)^2)\\binom{2k}{k}\\] for $k\\ge 3$. To do so, we build on a quasirandomness and induction framework for Ramsey numbers introduced by Thomason and extended by Conlon, demonstrating optimal \"effective quasirandomness\" results about convergence of graphs. This optimality represents a natural barrier to improvement.","url_abs":"http://arxiv.org/abs/2005.09251v1","url_pdf":"http://arxiv.org/pdf/2005.09251v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"diagonal-ramsey-via-effective-quasirandomness","repo_url":"https://github.com/lidangzzz/R55-is-NOT-43","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}