{
  "id": "1312.5627",
  "version": "v1",
  "published": "2013-12-19T16:35:41.000Z",
  "updated": "2013-12-19T16:35:41.000Z",
  "title": "Duality and syzygies for semimodules over numerical semigroups",
  "authors": [
    "Julio José Moyano-Fernández",
    "Jan Uliczka"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $\\Gamma=\\langle \\alpha, \\beta \\rangle$ be a numerical semigroup. In this article we consider the dual $\\Delta^*$ of a $\\Gamma$-semimodule $\\Delta$; in particular we deduce a formula that expresses the minimal set of generators of $\\Delta^*$ in terms of the generators of $\\Delta$. As applications we compute the minimal graded free resolution of a graded $\\mathbb{F}[t^{\\alpha},t^{\\beta}]$-submodule of $\\mathbb{F}[t]$, and we investigate the structure of the selfdual $\\Gamma$-semimodules, leading to a new way of counting them.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-12-19T16:35:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20M14",
      "05A19"
    ],
    "keywords": [
      "numerical semigroup",
      "semimodule",
      "minimal graded free resolution",
      "generators",
      "minimal set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1312.5627J"
    }
  }
}