{
  "id": "0710.3718",
  "version": "v1",
  "published": "2007-10-19T15:10:18.000Z",
  "updated": "2007-10-19T15:10:18.000Z",
  "title": "Weighted Sequences in Finite Cyclic Groups",
  "authors": [
    "David J. Grynkiewicz",
    "Jujuan Zhuang"
  ],
  "categories": [
    "math.CO",
    "math.NT"
  ],
  "abstract": "Let $p>7$ be a prime, let $G=\\Z/p\\Z$, and let $S_1=\\prod_{i=1}^p g_i$ and $S_2=\\prod_{i=1}^p h_i$ be two sequences with terms from $G$. Suppose that the maximum multiplicity of a term from either $S_1$ or $S_2$ is at most $\\frac{2p+1}{5}$. Then we show that, for each $g\\in G$, there exists a permutation $\\sigma$ of $1,2,..., p$ such that $g=\\sum_{i=1}^{p}(g_i\\cdot h_{\\sigma(i)})$. The question is related to a conjecture of A. Bialostocki concerning weighted subsequence sums and the Erd\\H{o}s-Ginzburg-Ziv Theorem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-10-19T15:10:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11B75",
      "11B50"
    ],
    "keywords": [
      "finite cyclic groups",
      "weighted sequences",
      "bialostocki concerning weighted subsequence sums",
      "maximum multiplicity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0710.3718G"
    }
  }
}