{
  "id": "1901.03937",
  "version": "v1",
  "published": "2019-01-13T06:30:57.000Z",
  "updated": "2019-01-13T06:30:57.000Z",
  "title": "M-Ambiguity Sequences for Parikh Matrices and Their Periodicity Revisited",
  "authors": [
    "Wen Chean Teh",
    "Ghajendran Poovanandran"
  ],
  "comment": "16 pages, submitted for publication consideration",
  "categories": [
    "math.CO"
  ],
  "abstract": "The introduction of Parikh matrices by Mateescu et al. in 2001 has sparked numerous new investigations in the theory of formal languages by various researchers, among whom is Serbanuta. Recently, a decade-old conjecture by Serbanuta on the M-ambiguity of words was disproved, leading to new possibilities in the study of such words. In this paper, we investigate how selective repeated duplications of letters in a word affect the M-ambiguity of the resulting words. The corresponding M-ambiguity of those words are then presented in sequences, which we term as M-ambiguity sequences. We show that nearly all patterns of M-ambiguity sequences are attainable. Finally, by employing certain algebraic approach and some underlying theory in integer programming, we show that repeated periodic duplications of letters of the same type in a word results in an M-ambiguity sequence that is eventually periodic.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-01-13T06:30:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "68R15",
      "68R05",
      "05A05"
    ],
    "keywords": [
      "m-ambiguity sequence",
      "parikh matrices",
      "periodicity",
      "formal languages",
      "repeated periodic duplications"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}