{"paper":{"title":"Random sum-free subsets of Abelian groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.PR"],"primary_cat":"math.CO","authors_text":"J\\'ozsef Balogh, Robert Morris, Wojciech Samotij","submitted_at":"2011-03-10T14:10:42Z","abstract_excerpt":"We characterize the structure of maximum-size sum-free subsets of a random subset of an Abelian group $G$. In particular, we determine the threshold $p_c \\approx \\sqrt{\\log n / n}$ above which, with high probability as $|G| \\to \\infty$, each such subset is contained in a maximum-size sum-free subset of $G$, whenever $q$ divides $|G|$ for some (fixed) prime $q$ with $q \\equiv 2 \\pmod 3$. Moreover, in the special case $G = \\ZZ_{2n}$, we determine a sharp threshold for the above property. The proof uses recent 'transference' theorems of Conlon and Gowers, together with stability theorems for sum-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.2041","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"}