{
  "id": "cond-mat/0604589",
  "version": "v1",
  "published": "2006-04-26T10:35:58.000Z",
  "updated": "2006-04-26T10:35:58.000Z",
  "title": "Spanning Trees on Lattices and Integration Identities",
  "authors": [
    "Shu-Chiuan Chang",
    "Wenya Wang"
  ],
  "comment": "15 pages, 3 figures, 1 table",
  "journal": "J. Phys. A: Math. Gen. 39, 10263-10275 (2006)",
  "doi": "10.1088/0305-4470/39/33/001",
  "categories": [
    "cond-mat.stat-mech",
    "math.CO"
  ],
  "abstract": "For a lattice $\\Lambda$ with $n$ vertices and dimension $d$ equal or higher than two, the number of spanning trees $N_{ST}(\\Lambda)$ grows asymptotically as $\\exp(n z_\\Lambda)$ in the thermodynamic limit. We present exact integral expressions for the asymptotic growth constant $z_\\Lambda$ for spanning trees on several lattices. By taking different unit cells in the calculation, many integration identities can be obtained. We also give $z_{\\Lambda (p)}$ on the homeomorphic expansion of $k$-regular lattices with $p$ vertices inserted on each edge.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-04-26T10:35:58.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "spanning trees",
      "integration identities",
      "exact integral expressions",
      "asymptotic growth constant",
      "thermodynamic limit"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Journal of Physics A Mathematical General",
      "year": 2006,
      "month": "Aug",
      "volume": 39,
      "number": 33,
      "pages": 10263
    },
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006JPhA...3910263C"
    }
  }
}