{
  "id": "math/0210170",
  "version": "v1",
  "published": "2002-10-11T08:22:39.000Z",
  "updated": "2002-10-11T08:22:39.000Z",
  "title": "Counting the occurrences of generalized patterns in words generated by a morphism",
  "authors": [
    "S. Kitaev",
    "T. Mansour"
  ],
  "comment": "6 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "We count the number of occurrences of certain patterns in given words. We choose these words to be the set of all finite approximations of a sequence generated by a morphism with certain restrictions. The patterns in our considerations are either classical patterns 1-2, 2-1, 1-1-...-1, or arbitrary generalized patterns without internal dashes, in which repetitions of letters are allowed. In particular, we find the number of occurrences of the patterns 1-2, 2-1, 12, 21, 123 and 1-1-...-1 in the words obtained by iterations of the morphism 1->123, 2->13, 3->2, which is a classical example of a morphism generating a nonrepetitive sequence.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2002-10-11T08:22:39.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "occurrences",
      "internal dashes",
      "arbitrary generalized patterns",
      "finite approximations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math.....10170K"
    }
  }
}