{"paper":{"title":"Sumfree sets in groups: a survey","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Terence Tao, Van Vu","submitted_at":"2016-03-09T21:49:31Z","abstract_excerpt":"We discuss several questions concerning sum-free sets in groups, raised by Erd\\H{o}s in his survey \"Extremal problems in number theory\" (Proceedings of the Symp. Pure Math. VIII AMS) published in 1965.\n  Among other things, we give a characterization for large sets $A$ in an abelian group $G$ which do not contain a subset $B$ of fixed size $k$ such that the sum of any two different elements of $B$ do not belong to $A$ (in other words, $B$ is sum-free with respect to $A$). Erd\\H{o}s, in the above mentioned survey, conjectured that if $|A|$ is sufficiently large compared to $k$, then $A$ contain"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.03071","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}