{
  "id": "2312.08273",
  "version": "v1",
  "published": "2023-12-13T16:43:40.000Z",
  "updated": "2023-12-13T16:43:40.000Z",
  "title": "Staircase graph words",
  "authors": [
    "Sela Fried",
    "Toufik Mansour"
  ],
  "comment": "14 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "Generalizing the notion of staircase words, introduced by Knopfmacher et.\\ al, we define staircase graph words. These are functions $w$ from the vertex set $V$ of a graph into the set $\\{1,2,\\ldots,k\\}$, such that $|w(x)-w(y)|\\leq 1$, for every adjacent $x,y\\in V$. We find the explicit generating functions for the number of staircase graph words for the grid graph, the rectangle-triangular graph and the king's graph, all of size $2\\times n$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-12-13T16:43:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "define staircase graph words",
      "grid graph",
      "explicit generating functions",
      "kings graph",
      "rectangle-triangular graph"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}