{
  "id": "1408.5331",
  "version": "v1",
  "published": "2014-08-22T15:41:09.000Z",
  "updated": "2014-08-22T15:41:09.000Z",
  "title": "On a conjecture of Wilf about the Frobenius number",
  "authors": [
    "Alessio Moscariello",
    "Alessio Sammartano"
  ],
  "comment": "6 pages",
  "categories": [
    "math.NT",
    "math.AC",
    "math.CO"
  ],
  "abstract": "Given coprime positive integers a_1 < ... < a_d, the Frobenius number F is the largest integer which is not representable as a non-negative integer combination of the a_i. Let n denote the number of integers less than F admitting such a representation: Wilf conjectured that F < nd. We prove that for every fixed value of floor(a_1/d) the conjecture holds for all values of a1 which are sufficiently large and are not divisible by a finite set of primes. We also propose a generalization in the context of one-dimensional local rings and a question on the equality F + 1 = nd.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-08-22T15:41:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11D07",
      "11B75",
      "20M14"
    ],
    "keywords": [
      "frobenius number",
      "one-dimensional local rings",
      "largest integer",
      "finite set",
      "non-negative integer combination"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1408.5331M"
    }
  }
}