{
  "id": "1701.07778",
  "version": "v1",
  "published": "2017-01-26T17:18:01.000Z",
  "updated": "2017-01-26T17:18:01.000Z",
  "title": "On Number of Rich Words",
  "authors": [
    "Josef Rukavicka"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "Any finite word $w$ of length $n$ contains at most $n+1$ distinct palindromic factors. If the bound $n+1$ is reached, the word $w$ is called rich. The number of rich words of length $n$ over an alphabet of cardinality $q$ is denoted $R_n(q)$. For binary alphabet, Rubinchik and Shur deduced that ${R_n(2)}\\leq c 1.605^n $ for some constant $c$. We prove that $\\lim\\limits_{n\\rightarrow \\infty }\\sqrt[n]{R_n(q)}=1$ for any $q$, i.e. $R_n(q)$ has a subexponential growth on any alphabet.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-01-26T17:18:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "68R15"
    ],
    "keywords": [
      "rich words",
      "distinct palindromic factors",
      "binary alphabet",
      "subexponential growth",
      "finite word"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}