{
  "id": "math/0610977",
  "version": "v1",
  "published": "2006-10-31T17:39:23.000Z",
  "updated": "2006-10-31T17:39:23.000Z",
  "title": "New results related to a conjecture of Manickam and Singhi",
  "authors": [
    "G. Chiaselotti",
    "G. Infante",
    "G. Marino"
  ],
  "doi": "10.1016/j.ejc.2007.03.002",
  "categories": [
    "math.CO"
  ],
  "abstract": "In 1998 Manickam and Singhi conjectured that for every positive integer $d$ and every $n \\ge 4d$, every set of $n$ real numbers whose sum is nonnegative contains at least $\\binom {n-1}{d-1}$ subsets of size $d$ whose sums are nonnegative. In this paper we establish new results related to this conjecture. We also prove that the conjecture of Manickam and Singhi does not hold for $n=2d+2$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-10-31T17:39:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05D05",
      "05A15"
    ],
    "keywords": [
      "conjecture",
      "real numbers",
      "positive integer"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math.....10977C"
    }
  }
}