{
  "id": "1105.1067",
  "version": "v1",
  "published": "2011-05-05T13:22:36.000Z",
  "updated": "2011-05-05T13:22:36.000Z",
  "title": "The 3-dimensional planar assignment problem and the number of Latin squares related to an autotopism",
  "authors": [
    "R. M. Falcón",
    "J. Martín-Morales"
  ],
  "comment": "4 pages, 1 table",
  "journal": "Proceedings of XI Spanish Meeting on Computational Algebra and Applications EACA 2008 (2008), pp. 89-92",
  "categories": [
    "math.CO"
  ],
  "abstract": "There exists a bijection between the set of Latin squares of order $n$ and the set of feasible solutions of the 3-dimensional planar assignment problem ($3PAP_n$). In this paper, we prove that, given a Latin square isotopism $\\Theta$, we can add some linear constraints to the $3PAP_n$ in order to obtain a 1-1 correspondence between the new set of feasible solutions and the set of Latin squares of order $n$ having $\\Theta$ in their autotopism group. Moreover, we use Gr\\\"obner bases in order to describe an algorithm that allows one to obtain the cardinal of both sets.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-05-05T13:22:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05B15",
      "20N05"
    ],
    "keywords": [
      "planar assignment problem",
      "latin squares",
      "feasible solutions",
      "latin square isotopism",
      "linear constraints"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1105.1067F"
    }
  }
}