{
  "id": "math/0512164",
  "version": "v2",
  "published": "2005-12-07T21:29:52.000Z",
  "updated": "2006-02-12T07:06:18.000Z",
  "title": "Around matrix-tree theorem",
  "authors": [
    "Yurii Burman",
    "Boris Shapiro"
  ],
  "comment": "13 pages, no figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "Generalizing the classical matrix-tree theorem we provide a formula counting subgraphs of a given graph with a fixed 2-core. We use this generalization to obtain an analog of the matrix-tree theorem for the root system $D_n$ (the classical theorem corresponds to the $A_n$-case). Several byproducts of the developed technique, such as a new formula for a specialization of the multivariate Tutte polynomial, are of independent interest.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2006-02-12T07:06:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C50",
      "05B35"
    ],
    "keywords": [
      "multivariate tutte polynomial",
      "classical matrix-tree theorem",
      "formula counting subgraphs",
      "classical theorem corresponds",
      "independent interest"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math.....12164B"
    }
  }
}