{
  "id": "1710.02848",
  "version": "v1",
  "published": "2017-10-08T16:09:24.000Z",
  "updated": "2017-10-08T16:09:24.000Z",
  "title": "Walks in the quarter plane, genus zero case",
  "authors": [
    "Thomas Dreyfus",
    "Charlotte Hardouin",
    "Julien Roques",
    "Michael F. Singer"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "In the present paper, we use Galois theory of difference equations to study the nature of the generating series of (weighted) walks in the quarter plane with genus zero kernel. Using this approach, we are able to prove that the generating series do not satisfy any nontrivial nonlinear algebraic differential equation with rational coefficients.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-10-08T16:09:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A15",
      "30D05",
      "39A06"
    ],
    "keywords": [
      "genus zero case",
      "quarter plane",
      "nontrivial nonlinear algebraic differential equation",
      "generating series",
      "genus zero kernel"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}