{"paper":{"title":"On the Minimum Size of Signed Sumsets in Elementary Abelian Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Bela Bajnok, Ryan Matzke","submitted_at":"2014-12-04T10:24:20Z","abstract_excerpt":"For a finite abelian group $G$ and positive integers $m$ and $h$, we let $$\\rho(G, m, h) = \\min \\{|hA| \\; : \\; A \\subseteq G, |A|=m\\}$$ and $$\\rho_{\\pm} (G, m, h) = \\min \\{|h_{\\pm} A| \\; : \\; A \\subseteq G, |A|=m\\},$$ where $hA$ and $h_{\\pm} A$ denote the $h$-fold sumset and the $h$-fold signed sumset of $A$, respectively. The study of $\\rho(G, m, h)$ has a 200-year-old history and is now known for all $G$, $m$, and $h$. In previous work we provided an upper bound for $\\rho_{\\pm} (G, m, h)$ that we believe is exact, and proved that $\\rho_{\\pm} (G, m, h)$ agrees with $\\rho (G, m, h)$ when $G$ i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.1609","kind":"arxiv","version":1},"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"}