Print Email Facebook Twitter On large subsets of Fnq with no three-termarithmetic progression Title On large subsets of Fnq with no three-termarithmetic progression Author Ellenberg, Jordan S. (University of Wisconsin-Madison) Gijswijt, Dion (TU Delft Discrete Mathematics and Optimization) Date 2017 Abstract In this note, we show that the method of Croot, Lev, and Pach can be used to bound the size of a subset of F n q Fqn with no three terms in arithmetic progression by c n cn with c<q c<q . For q=3 q=3 , the problem of finding the largest subset of F n 3 F3n with no three terms in arithmetic progression is called the cap set problem. Previously the best known upper bound for the affine cap problem, due to Bateman and Katz, was on order n −1−ϵ 3 n n−1−ϵ3n . Subject additive combinatoricsadditive number theoryarithmetic progressionscap sets To reference this document use: http://resolver.tudelft.nl/uuid:24934b91-cb43-49ef-9423-731dd1fb9306 DOI https://doi.org/10.4007/annals.2017.185.1.8 ISSN 0003-4865 Source Annals of Mathematics, 185 (1), 339-343 Bibliographical note Accepted author manuscript Part of collection Institutional Repository Document type journal article Rights © 2017 Jordan S. Ellenberg, Dion Gijswijt Files PDF Cap_Set_3.pdf 234.98 KB Close viewer /islandora/object/uuid:24934b91-cb43-49ef-9423-731dd1fb9306/datastream/OBJ/view