{
  "id": "math/0603608",
  "version": "v1",
  "published": "2006-03-26T13:31:56.000Z",
  "updated": "2006-03-26T13:31:56.000Z",
  "title": "Palindromic complexity of infinite words associated with simple Parry numbers",
  "authors": [
    "Petr Ambrož",
    "Christiane Frougny",
    "Zuzana Masáková",
    "Edita Pelantová"
  ],
  "comment": "28 pages, to appear in Annales de l'Institut Fourier",
  "categories": [
    "math.CO",
    "math.NT"
  ],
  "abstract": "A simple Parry number is a real number \\beta>1 such that the R\\'enyi expansion of 1 is finite, of the form d_\\beta(1)=t_1...t_m. We study the palindromic structure of infinite aperiodic words u_\\beta that are the fixed point of a substitution associated with a simple Parry number \\beta. It is shown that the word u_\\beta contains infinitely many palindromes if and only if t_1=t_2= ... =t_{m-1} \\geq t_m. Numbers \\beta satisfying this condition are the so-called confluent Pisot numbers. If t_m=1 then u_\\beta is an Arnoux-Rauzy word. We show that if \\beta is a confluent Pisot number then P(n+1)+ P(n) = C(n+1) - C(n)+ 2, where P(n) is the number of palindromes and C(n) is the number of factors of length n in u_\\beta. We then give a complete description of the set of palindromes, its structure and properties.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-03-26T13:31:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "68R15",
      "11A63"
    ],
    "keywords": [
      "simple parry number",
      "infinite words",
      "palindromic complexity",
      "confluent pisot number",
      "infinite aperiodic words"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......3608A"
    }
  }
}