{"paper":{"title":"A New Proof of Kemperman's Theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Amanda Montejano, Matt DeVos, Tomas Boothby","submitted_at":"2013-01-01T15:33:00Z","abstract_excerpt":"Let $G$ be an additive abelian group and let $A,B \\subseteq G$ be finite and nonempty. The pair $(A,B)$ is called critical if the sumset $A+B = {a+b \\mid $a \\in A$ and $b\\in B$}$ satisfies $|A+B| < |A| + |B|$. Vosper proved a theorem which characterizes all critical pairs in the special case when $|G|$ is prime. Kemperman generalized this by proving a structure theorem for critical pairs in an arbitrary abelian group. Here we give a new proof of Kemperman's Theorem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.0095","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"}