{
  "id": "1208.5993",
  "version": "v3",
  "published": "2012-08-29T19:08:36.000Z",
  "updated": "2012-12-12T21:36:42.000Z",
  "title": "Γ-species and the enumeration of k-trees",
  "authors": [
    "Andrew Gainer-Dewar"
  ],
  "comment": "26 pages; includes Python code",
  "journal": "Electronic Journal of Combinatorics, 19(4) (2012), #P45",
  "categories": [
    "math.CO"
  ],
  "abstract": "We study the class of graphs known as k-trees through the lens of Joyal's theory of combinatorial species (and an equivariant extension known as '$\\Gamma$-species' which incorporates data about 'structural' group actions). This culminates in a system of recursive functional equations giving the generating function for unlabeled k-trees which allows for fast, efficient computation of their numbers. Enumerations up to k = 10 and n = 30 (for a k-tree with (n+k-1) vertices) are included in tables, and Sage code for the general computation is included in an appendix.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2012-12-12T21:36:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C30",
      "05E18"
    ],
    "keywords": [
      "enumeration",
      "combinatorial species",
      "equivariant extension",
      "incorporates data",
      "group actions"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1208.5993G"
    }
  }
}