{"paper":{"title":"Comments on Y. O. Hamidoune's Paper \"Adding Distinct Congruence Classes\"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"B\\'ela Bajnok","submitted_at":"2015-12-09T20:46:56Z","abstract_excerpt":"The main result in Y.~O.~Hamidoune's paper \"Adding Distinct Congruence Classes\" ({\\em Combin.~Probab.~Comput.}~{\\bf 7} (1998) 81-87) is as follows: If $S$ is a generating subset of a cyclic group $G$ such that $0 \\not \\in S$ and $|S| \\geq 5$, then the number of sums of the subsets of $S$ is at least $\\min (|G|, 2|S| )$. Unfortunately, argument of the author, who, sadly, passed away in 2011, relies on a lemma whose proof is incorrect; in fact, the lemma is false for all cyclic groups of even order. In this short note we point out this mistake, correct the proof, and discuss why the main result "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.03040","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"}