{
  "id": "2308.04155",
  "version": "v1",
  "published": "2023-08-08T09:36:50.000Z",
  "updated": "2023-08-08T09:36:50.000Z",
  "title": "A short note on the order of the double reduced 2-factor transfer digraph for rectangular grid graphs",
  "authors": [
    "Jelena Đokic"
  ],
  "comment": "8 pages, 3 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "We prove that the order of the double reduced 2-factor transfer digraph ${\\cal R}^{**}_{m}$ which is needed for the enumeration of the spanning unions of cycles in the rectangular grid graph $P_m \\times P_n$ ($m,n \\in N$), when $m$ is odd, is equal to $\\displaystyle \\mid V({\\cal R}^{**}_{m}) \\mid = \\frac{1}{2} \\left[{m+1 \\choose (m-1)/2 } + {(m+1)/2 \\choose \\lfloor (m+1)/4 \\rfloor}\\right].$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-08-08T09:36:50.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "rectangular grid graph",
      "transfer digraph",
      "short note",
      "spanning unions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}