{
  "id": "2102.00443",
  "version": "v1",
  "published": "2021-01-31T13:04:54.000Z",
  "updated": "2021-01-31T13:04:54.000Z",
  "title": "Pattern occurrences in $k$-ary words revisited: a few new and old observations",
  "authors": [
    "Toufik Mansour",
    "Reza Rastegar"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "In this paper, we study the pattern occurrence in $k$-ary words. We prove an explicit upper bound on the number of $k$-ary words avoiding any given pattern using a random walk argument. Additionally, we reproduce several already known results and establish a simple connection among pattern occurrences in permutations and $k$-ary words. A simple consequence of this connection is that Wilf-equivalence of two patterns in words implies their Wilf-equivalence in permutations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-01-31T13:04:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A05",
      "05A16",
      "05C81"
    ],
    "keywords": [
      "ary words",
      "pattern occurrence",
      "old observations",
      "random walk argument",
      "explicit upper bound"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}