{
  "id": "1211.3269",
  "version": "v1",
  "published": "2012-11-14T10:52:09.000Z",
  "updated": "2012-11-14T10:52:09.000Z",
  "title": "Integer Points in Knapsack Polytopes and s-covering Radius",
  "authors": [
    "Iskander Aliev",
    "Martin Henk",
    "Eva Linke"
  ],
  "categories": [
    "math.CO",
    "math.NT",
    "math.OC"
  ],
  "abstract": "Given an integer matrix A satisfying certain regularity assumptions, we consider for a positive integer s the set F_s(A) of all integer vectors b such that the associated knapsack polytope P(A,b)={x: Ax=b, x non-negative} contains at least s integer points. In this paper we investigate the structure of the set F_s(A) sing the concept of s-covering radius. In particular, in a special case we prove an optimal lower bound for the s-Frobenius number.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-11-14T10:52:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "90C10",
      "52C07",
      "11D07",
      "90C27",
      "11H06"
    ],
    "keywords": [
      "integer points",
      "s-covering radius",
      "optimal lower bound",
      "associated knapsack polytope",
      "integer vectors"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1211.3269A"
    }
  }
}