{
  "id": "cond-mat/0602574",
  "version": "v1",
  "published": "2006-02-24T01:18:49.000Z",
  "updated": "2006-02-24T01:18:49.000Z",
  "title": "Some Exact Results for Spanning Trees on Lattices",
  "authors": [
    "Shu-Chiuan Chang",
    "Robert Shrock"
  ],
  "comment": "7 pages, 1 table",
  "journal": "J. Phys. A: Math. Gen. 39, 5653-5658 (2006)",
  "doi": "10.1088/0305-4470/39/20/001",
  "categories": [
    "cond-mat.stat-mech",
    "math.CO"
  ],
  "abstract": "For $n$-vertex, $d$-dimensional lattices $\\Lambda$ with $d \\ge 2$, the number of spanning trees $N_{ST}(\\Lambda)$ grows asymptotically as $\\exp(n z_\\Lambda)$ in the thermodynamic limit. We present an exact closed-form result for the asymptotic growth constant $z_{bcc(d)}$ for spanning trees on the $d$-dimensional body-centered cubic lattice. We also give an exact integral expression for $z_{fcc}$ on the face-centered cubic lattice and an exact closed-form expression for $z_{488}$ on the $4 \\cdot 8 \\cdot 8$ lattice.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-02-24T01:18:49.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "spanning trees",
      "exact results",
      "dimensional body-centered cubic lattice",
      "exact integral expression",
      "asymptotic growth constant"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}