{
  "id": "1206.6750",
  "version": "v3",
  "published": "2012-06-28T16:15:08.000Z",
  "updated": "2013-12-03T14:59:59.000Z",
  "title": "Solving multivariate functional equations",
  "authors": [
    "Michael Chon",
    "Christopher R. H. Hanusa",
    "Amy Lee"
  ],
  "comment": "11 pages, 1 figure. v3: Main theorems and writing style revised for greater clarity. Updated to final version, to appear in Discrete Mathematics",
  "doi": "10.1016/j.disc.2013.11.023",
  "categories": [
    "math.CO"
  ],
  "abstract": "This paper presents a new method to solve functional equations of multivariate generating functions, such as $$F(r,s)=e(r,s)+xf(r,s)F(1,1)+xg(r,s)F(qr,1)+xh(r,s)F(qr,qs),$$ giving a formula for $F(r,s)$ in terms of a sum over finite sequences. We use this method to show how one would calculate the coefficients of the generating function for parallelogram polyominoes, which is impractical using other methods. We also apply this method to answer a question from fully commutative affine permutations.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2013-12-03T14:59:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65Q20",
      "05A15",
      "05A05",
      "05B50",
      "05C38",
      "05E15"
    ],
    "keywords": [
      "solving multivariate functional equations",
      "finite sequences",
      "multivariate generating functions",
      "fully commutative affine permutations",
      "parallelogram polyominoes"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1206.6750C"
    }
  }
}