{"paper":{"title":"On the maximal multiplicity of long zero-sum free sequences over $C_p\\oplus C_p$","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Linlin Wang, Qinghai Zhong, Yushuang Fan","submitted_at":"2012-11-22T08:27:12Z","abstract_excerpt":"In this paper, we point out that the method used in [Acta Arith. 128(2007) 245-279] can be modified slightly to obtain the following result. Let $\\varepsilon \\in (0,\\frac 14)$ and $c>0$, and let $p$ be a sufficiently large prime depending on $\\varepsilon$ and $c$. Then every zero-sumfree sequence $S$ over $C_p\\oplus C_p$ of length $|S|\\geq 2p-c\\sqrt{p}$ contains some element at least $\\lfloor p^{\\frac14-\\varepsilon}\\rfloor$ times."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.5226","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"}