{"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/a-construction-for-difference-sets-with-local","title":"A Construction for Difference Sets with Local Properties","arxiv_id":"1812.07651","date":"2018-12-18","proceeding":null,"authors":["Sara Fish","Ben Lund","Adam Sheffer"],"abstract":"We construct finite sets of real numbers that have a small difference set and strong local properties. In particular, we construct a set $A$ of $n$ real numbers such that $|A-A|=n^{\\log_2 3}$ and that every subset $A'\\subseteq A$ of size $k$ satisfies $|A'-A'|\\ge k^{\\log_2 3}$. This construction leads to the first non-trivial upper bound for the problem of distinct distances with local properties.","url_abs":"https://arxiv.org/abs/1812.07651v1","url_pdf":"https://arxiv.org/pdf/1812.07651v1.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":"a-construction-for-difference-sets-with-local","repo_url":"https://github.com/the-set-of-sets/local-properties","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}