{"paper":{"title":"The Cardinality of Sumsets: Different Summands","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Brendan Murphy, Eyvindur Ari Palsson, Giorgis Petridis","submitted_at":"2013-09-09T15:23:56Z","abstract_excerpt":"Let $h$ be a positive integer and $A, B_1, B_2,\\dots, B_h$ be finite sets in a commutative group. We bound $|A+B_1+...+B_h|$ from above in terms of $|A|, |A+B_1|,\\dots,|A+B_h|$ and $h$. Extremal examples, which demonstrate that the bound is asymptotically sharp in all the parameters, are furthermore provided."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.2191","kind":"arxiv","version":3},"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"}