{"paper":{"title":"Iterated Sumsets and Subsequence Sums","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"David J. Grynkiewicz","submitted_at":"2017-09-26T23:52:54Z","abstract_excerpt":"Let $G\\cong \\mathbb Z/m_1\\mathbb Z\\times\\ldots\\times \\mathbb Z/m_r\\mathbb Z$ be a finite abelian group with $m_1\\mid\\ldots\\mid m_r=\\exp(G)$. The Kemperman Structure Theorem characterizes all subsets $A,\\,B\\subseteq G$ satisfying $|A+B|<|A|+|B|$ and has been extended to cover the case when $|A+B|\\leq |A|+|B|$. Utilizing these results, we provide a precise structural description of all finite subsets $A\\subseteq G$ with $|nA|\\leq (|A|+1)n-3$ when $n\\geq 3$ (also when $G$ is infinite), in which case many of the pathological possibilities from the case $n=2$ vanish, particularly for large $n\\geq \\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.09285","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"}