{
  "id": "1010.5101",
  "version": "v2",
  "published": "2010-10-25T12:38:28.000Z",
  "updated": "2011-03-04T02:39:56.000Z",
  "title": "On the Erd{\\H o}s--Ginzburg--Ziv constant of finite abelian groups of high rank",
  "authors": [
    "Yushuang Fan",
    "Weidong Gao",
    "Qinghai Zhong"
  ],
  "comment": "10 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $G$ be a finite abelian group. The Erd{\\H o}s--Ginzburg--Ziv constant $\\mathsf s (G)$ of $G$ is defined as the smallest integer $l \\in \\mathbb N$ such that every sequence \\ $S$ \\ over $G$ of length $|S| \\ge l$ \\ has a zero-sum subsequence $T$ of length $|T| = \\exp (G)$. If $G$ has rank at most two, then the precise value of $\\mathsf s (G)$ is known (for cyclic groups this is the Theorem of Erd{\\H o}s-Ginzburg-Ziv). Only very little is known for groups of higher rank. In the present paper, we focus on groups of the form $G = C_n^r$, with $n, r \\in \\N$ and $n \\ge 2$, and we tackle the study of $\\mathsf s (G)$ with a new approach, combining the direct problem with the associated inverse problem.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-03-04T02:39:56.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite abelian group",
      "s-ginzburg-ziv constant",
      "high rank",
      "associated inverse problem",
      "smallest integer"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1010.5101F"
    }
  }
}