{"paper":{"title":"A quadratic lower bound for subset sums","license":"","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Bojan Mohar, Luis Goddyn, Matt DeVos, Robert Samal (Simon Fraser University)","submitted_at":"2006-12-02T04:20:48Z","abstract_excerpt":"Let A be a finite nonempty subset of an additive abelian group G, and let \\Sigma(A) denote the set of all group elements representable as a sum of some subset of A. We prove that |\\Sigma(A)| >= |H| + 1/64 |A H|^2 where H is the stabilizer of \\Sigma(A). Our result implies that \\Sigma(A) = Z/nZ for every set A of units of Z/nZ with |A| >= 8 \\sqrt{n}. This consequence was first proved by Erd\\H{o}s and Heilbronn for n prime, and by Vu (with a weaker constant) for general n."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0612045","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"}