{"paper":{"title":"On Davenport constant of finite abelian groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Dongchun Han","submitted_at":"2018-02-20T16:52:11Z","abstract_excerpt":"$G$ be an additive finite abelian group. The Davenport constant $\\mathsf D(G)$ is the smallest integer $t$ such that every sequence (multiset) $S$ over $G$ of length $|S|\\ge t$ has a non-empty zero-sum subsequence. Recently, B. Girard proved that for every fixed integer $r > 1$ the Davenport constant $\\mathsf D(C_n^r)$ is asymptotic to $rn$ when $n$ tends to infinity. In this paper, for every fixed positive integer $r$, we prove that\n$$\\mathsf D(C_n^r)=rn+O(\\frac{n}{\\ln n}).$$\nThis is an explicit version of the above result of B. Girard. Furthermore, we can get better estimates of the error te"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.07196","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"}