{
  "id": "1101.4112",
  "version": "v1",
  "published": "2011-01-21T11:30:44.000Z",
  "updated": "2011-01-21T11:30:44.000Z",
  "title": "Integer Programming and m-irreducibility of numerical semigroups",
  "authors": [
    "Víctor Blanco",
    "Justo Puerto"
  ],
  "comment": "22 pages",
  "categories": [
    "math.OC",
    "math.AC"
  ],
  "abstract": "This paper addresses the problem of decomposing a numerical semigroup into m-irreducible numerical semigroups. The problem originally stated in algebraic terms is translated, introducing the so called Kunz-coordinates, to resolve a series of several discrete optimization problems. First, we prove that finding a minimal m-irreducible decomposition is equivalent to solve a multiobjective linear integer problem. Then, we restate that problem as the problem of finding all the optimal solutions of a finite number of single objective integer linear problems plus a set covering problem. Finally, we prove that there is a suitable transformation that reduces the original problem to find an optimal solution of a compact integer linear problem. This result ensures a polynomial time algorithm for each given multiplicity m. We have implemented the different algorithms and have performed some computational experiments to show the efficiency of our methodology.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-01-21T11:30:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "90C10",
      "20M14",
      "11D75"
    ],
    "keywords": [
      "numerical semigroup",
      "integer programming",
      "compact integer linear problem",
      "optimal solution",
      "objective integer linear problems plus"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1101.4112B"
    }
  }
}