{"paper":{"title":"On n-sum of an abelian group of order n","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Weidong Gao, Xingwu Xia","submitted_at":"2013-08-11T05:07:57Z","abstract_excerpt":"Let $G$ be an additive finite abelian group of order $n$, and let $S$ be a sequence of $n+k$ elements in $G$, where $k\\geq 1$. Suppose that $S$ contains $t$ distinct elements. Let $\\sum_n(S)$ denote the set that consists of all elements in $G$ which can be expressed as the sum over a subsequence of length $n$. In this paper we prove that, either $0\\in \\sum_n(S)$ or $|\\sum_n(S)|\\geq k+t-1.$ This confirms a conjecture by Y.O. Hamidoune in 2000."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.2365","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"}