{"paper":{"title":"Sum-avoiding sets in groups","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Terence Tao, Van Vu","submitted_at":"2016-03-09T21:43:24Z","abstract_excerpt":"Let $A$ be a finite subset of an arbitrary additive group $G$, and let $\\phi(A)$ denote the cardinality of the largest subset $B$ in $A$ that is sum-avoiding in $A$ (that is to say, $b_1+b_2 \\not \\in A$ for all distinct $b_1,b_2 \\in B$). The question of controlling the size of $A$ in terms of $\\phi(A)$ in the case when $G$ was torsion-free was posed by Erd\\H{o}s and Moser. When $G$ has torsion, $A$ can be arbitrarily large for fixed $\\phi(A)$ due to the presence of subgroups. Nevertheless, we provide a qualitative answer to an analogue of the Erd\\H{o}s-Moser problem in this setting, by establi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.03068","kind":"arxiv","version":5},"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"}