{
  "id": "2011.01067",
  "version": "v1",
  "published": "2020-11-02T15:52:34.000Z",
  "updated": "2020-11-02T15:52:34.000Z",
  "title": "Asymptotic behavior of Integer Programming and the stability of the Castelnuovo-Mumford regularity",
  "authors": [
    "Le Tuan Hoa"
  ],
  "comment": "33 pages; submitted to Math. Programming",
  "categories": [
    "math.AC",
    "math.OC"
  ],
  "abstract": "The paper provides a connection between Commutative Algebra and Integer Programming and contains two parts. The first one is devoted to the asymptotic behavior of integer programs with a fixed cost linear functional and the constraint sets consisting of a finite system of linear equations or inequalities with integer coefficients depending linearly on $n$. An integer $N_*$ is determined such that the optima of these integer programs are a quasi-linear function of $n$ for all $n\\ge N_*$. Using results in the first part, one can bound in the second part the indices of stability of the Castelnuovo-Mumford regularities of integral closures of powers of a monomial ideal and that of symbolic powers of a square-free monomial ideal.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-11-02T15:52:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "13D45",
      "90C10"
    ],
    "keywords": [
      "castelnuovo-mumford regularity",
      "asymptotic behavior",
      "integer programming",
      "integer programs",
      "fixed cost linear functional"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}