{
  "id": "math/0304465",
  "version": "v1",
  "published": "2003-04-28T20:15:16.000Z",
  "updated": "2003-04-28T20:15:16.000Z",
  "title": "Singular combinatorics",
  "authors": [
    "Philippe Flajolet"
  ],
  "journal": "Proceedings of the ICM, Beijing 2002, vol. 3, 561--572",
  "categories": [
    "math.CO"
  ],
  "abstract": "Combinatorial enumeration leads to counting generating functions presenting a wide variety of analytic types. Properties of generating functions at singularities encode valuable information regarding asymptotic counting and limit probability distributions present in large random structures. ``Singularity analysis'' reviewed here provides constructive estimates that are applicable in several areas of combinatorics. It constitutes a complex-analytic Tauberian procedure by which combinatorial constructions and asymptotic--probabilistic laws can be systematically related.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-04-28T20:15:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A15",
      "05A16",
      "30B10",
      "39B05",
      "60C05",
      "60F05",
      "68Q25"
    ],
    "keywords": [
      "singular combinatorics",
      "information regarding asymptotic counting",
      "encode valuable information regarding asymptotic",
      "generating functions",
      "complex-analytic tauberian procedure"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......4465F"
    }
  }
}