{
  "id": "math/0104241",
  "version": "v1",
  "published": "2001-04-25T15:42:27.000Z",
  "updated": "2001-04-25T15:42:27.000Z",
  "title": "The Laurent phenomenon",
  "authors": [
    "Sergey Fomin",
    "Andrei Zelevinsky"
  ],
  "comment": "21 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "A composition of birational maps given by Laurent polynomials need not be given by Laurent polynomials; however, sometimes---quite unexpectedly---it does. We suggest a unified treatment of this phenomenon, which covers a large class of applications. In particular, we settle in the affirmative a conjecture of D.Gale and R.Robinson on integrality of generalized Somos sequences, and prove the Laurent property for several multidimensional recurrences, confirming conjectures by J.Propp, N.Elkies, and M.Kleber.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2001-04-25T15:42:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14E05"
    ],
    "keywords": [
      "laurent phenomenon",
      "sometimes-quite unexpectedly-it",
      "birational maps",
      "multidimensional recurrences",
      "conjecture"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2001math......4241F"
    }
  }
}