{
  "id": "1101.4492",
  "version": "v1",
  "published": "2011-01-24T10:43:37.000Z",
  "updated": "2011-01-24T10:43:37.000Z",
  "title": "On the number of subsequences with a given sum in a finite abelian group",
  "authors": [
    "Gerard Jennhwa Chang",
    "Sheng-Hua Chen",
    "Yongke Qu",
    "Guoqing Wang",
    "Haiyan Zhang"
  ],
  "comment": "9 pages",
  "categories": [
    "math.CO",
    "math.NT"
  ],
  "abstract": "Suppose $G$ is a finite abelian group and $S$ is a sequence of elements in $G$. For any element $g$ of $G$, let $N_g(S)$ denote the number of subsequences of $S$ with sum $g$. The purpose of this paper is to investigate the lower bound for $N_g(S)$. In particular, we prove that either $N_g(S)=0$ or $N_g(S) \\ge 2^{|S|-D(G)+1}$, where $D(G)$ is the smallest positive integer $\\ell$ such that every sequence over $G$ of length at least $\\ell$ has a nonempty zero-sum subsequence. We also characterize the structures of the extremal sequences for which the equality holds for some groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-01-24T10:43:37.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite abelian group",
      "nonempty zero-sum subsequence",
      "smallest positive integer",
      "equality holds",
      "extremal sequences"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1101.4492J"
    }
  }
}