{"paper":{"title":"Zero-sum Subsequences of Length kq over Finite Abelian p-Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CO","authors_text":"Xiaoyu He","submitted_at":"2015-03-24T03:54:18Z","abstract_excerpt":"For a finite abelian group $G$ and a positive integer $k$, let $s_{k}(G)$ denote the smallest integer $\\ell\\in\\mathbb{N}$ such that any sequence $S$ of elements of $G$ of length $|S|\\geq\\ell$ has a zero-sum subsequence with length $k$. The celebrated Erd\\H{o}s-Ginzburg-Ziv theorem determines $s_{n}(C_{n})=2n-1$ for cyclic groups $C_{n}$, while Reiher showed in 2007 that $s_{n}(C_{n}^{2})=4n-3$. In this paper we prove for a $p$-group $G$ with exponent $\\exp(G)=q$ the upper bound $s_{kq}(G)\\le(k+2d-2)q+3D(G)-3$ whenever $k\\geq d$, where $d=\\Big\\lceil\\frac{D(G)}{q}\\Big\\rceil$ and $p$ is a prime s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.06905","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"}