{
  "id": "1407.7774",
  "version": "v2",
  "published": "2014-07-29T16:57:36.000Z",
  "updated": "2015-01-27T17:04:39.000Z",
  "title": "Matrix integrals and generating functions for permutations and one-face rooted hypermaps",
  "authors": [
    "Jacob P. Dyer"
  ],
  "comment": "19 pages, 4 figures",
  "categories": [
    "math.CO",
    "math-ph",
    "math.MP"
  ],
  "abstract": "Closed-form generating functions for counting one-face rooted hypermaps with a known number of darts by number of vertices and edges is found, using matrix integral expressions relating to the reduced density operator of a bipartite quantum system. A recursion relation for these generating functions is also found. The method for computing similar generating functions for two-face rooted hypermaps by number of vertices and edges is outlined.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-07-29T16:57:36.000Z",
      "abstract": "Closed-form generating functions for counting one-face rooted hypermaps with a known number of darts by number of vertices and edges is found, using matrix integral expressions relating to the reduced density operator of a bipartite quantum system. Generating functions for counting permutations by number of cycles and counting two-face rooted hypermaps by number of vertices and edges are also derived by similar methods.",
      "comment": "17 pages, 4 figures",
      "journal": null,
      "doi": null,
      "authors": [
        "Jacob P Dyer"
      ]
    },
    {
      "version": "v2",
      "updated": "2015-01-27T17:04:39.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "permutations",
      "bipartite quantum system",
      "closed-form generating functions",
      "matrix integral expressions relating",
      "counting one-face rooted hypermaps"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1407.7774D"
    }
  }
}