{
  "id": "1807.06171",
  "version": "v1",
  "published": "2018-07-17T01:20:13.000Z",
  "updated": "2018-07-17T01:20:13.000Z",
  "title": "Parikh Motivated Study on Repetitions in Words",
  "authors": [
    "Ghajendran Poovanandran",
    "Adrian Atanasiu",
    "Wen Chean Teh"
  ],
  "comment": "15 pages, preprint submitted",
  "categories": [
    "math.CO"
  ],
  "abstract": "We introduce the notion of general prints of a word, which is substantialized by certain canonical decompositions, to study repetition in words. These associated decompositions, when applied recursively on a word, result in what we term as core prints of the word. The length of the path to attain a core print of a general word is scrutinized. This paper also studies the class of square-free ternary words with respect to the Parikh matrix mapping, which is an extension of the classical Parikh mapping. It is shown that there are only finitely many matrix-equivalence classes of ternary words such that all words in each class are square-free. Finally, we employ square-free morphisms to generate infinitely many pairs of square-free ternary words that share the same Parikh matrix.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-07-17T01:20:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "68R15",
      "68Q45",
      "05A05"
    ],
    "keywords": [
      "parikh motivated study",
      "square-free ternary words",
      "core print",
      "parikh matrix",
      "employ square-free morphisms"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}