{"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/nearly-all-k-sat-functions-are-unate","title":"Nearly all $k$-SAT functions are unate","arxiv_id":"2209.04894","date":"2022-09-11","proceeding":null,"authors":["József Balogh","Dingding Dong","Bernard Lidický","Nitya Mani","Yufei Zhao"],"abstract":"We prove that $1-o(1)$ fraction of all $k$-SAT functions on $n$ Boolean variables are unate (i.e., monotone after first negating some variables), for any fixed positive integer $k$ and as $n \\to \\infty$. This resolves a conjecture by Bollob\\'as, Brightwell, and Leader from 2003.","url_abs":"https://arxiv.org/abs/2209.04894v2","url_pdf":"https://arxiv.org/pdf/2209.04894v2.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":"nearly-all-k-sat-functions-are-unate","repo_url":"https://github.com/thingarfield/density-k-pdg","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}