{"paper":{"title":"An improved bound on $(A+A)/(A+A)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ben Lund","submitted_at":"2016-06-10T20:28:21Z","abstract_excerpt":"We show that, for a finite set $A$ of real numbers, the size of the set $$\\frac{A+A}{A+A} = \\left\\{ \\frac{a+b}{c+d} : a,b,c,d \\in A, c+d \\neq 0 \\right \\}$$ is bounded from below by $$\\left|\\frac{A+A}{A+A} \\right| \\gg \\frac{|A|^{2+1/4}}{|A / A|^{1/8} \\log |A|}.$$ This improves a result of Roche-Newton."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.03468","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"}