{
  "id": "1604.04642",
  "version": "v1",
  "published": "2016-04-15T20:54:30.000Z",
  "updated": "2016-04-15T20:54:30.000Z",
  "title": "Asymptotics of Bivariate Analytic Functions with Algebraic Singularities",
  "authors": [
    "Torin Greenwood"
  ],
  "comment": "31 pages, 4 figures. An extended abstract will appear in the conference proceedings for the 28th International Conference on Formal Power Series and Algebraic Combinatorics",
  "categories": [
    "math.CO"
  ],
  "abstract": "In this paper, we use the multivariate analytic techniques of Pemantle and Wilson to derive asymptotic formulae for the coefficients of a broad class of multivariate generating functions with algebraic singularities. Flajolet and Odlyzko (1990) analyzed the coefficients of a class of univariate generating functions with algebraic singularities. These results have been extended to classes of multivariate generating functions by Gao and Richmond (1992) and Hwang (1996, 1998), in both cases by immediately reducing the multivariate case to the univariate case. Pemantle and Wilson (2013) outlined new multivariate analytic techniques and used them to analyze the coefficients of rational generating functions. These same multivariate techniques can be used to analyze functions with algebraic singularities.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-04-15T20:54:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A16",
      "05A15"
    ],
    "keywords": [
      "algebraic singularities",
      "bivariate analytic functions",
      "multivariate analytic techniques",
      "multivariate generating functions",
      "coefficients"
    ],
    "tags": [
      "conference paper"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}