{
  "id": "0904.4065",
  "version": "v2",
  "published": "2009-04-26T21:43:16.000Z",
  "updated": "2011-04-07T00:25:29.000Z",
  "title": "Combinatorics of Cremona monomial maps",
  "authors": [
    "Aron Simis",
    "Rafael H. Villarreal"
  ],
  "comment": "Mathematics of Computation, to appear",
  "journal": "Math. Comp. 81 (2012), no. 279, 1857--1867",
  "categories": [
    "math.AG",
    "math.AC",
    "math.CO"
  ],
  "abstract": "One studies Cremona monomial maps by combinatorial means. Among the results is a simple integer matrix theoretic proof that the inverse of a Cremona monomial map is also defined by monomials of fixed degree, and moreover, the set of monomials defining the inverse can be obtained explicitly in terms of the initial data. A neat consequence is drawn for the plane Cremona monomial group, in particular the known result saying that a plane Cremona (monomial) map and its inverse have the same degree. Included is a discussion about the computational side and/or implementation of the combinatorial invariants stemming from these questions.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-04-07T00:25:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14E05",
      "14E07"
    ],
    "keywords": [
      "simple integer matrix theoretic proof",
      "combinatorics",
      "studies cremona monomial maps",
      "plane cremona monomial group",
      "neat consequence"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AMS",
      "journal": "Math. Comp."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0904.4065S"
    }
  }
}