{
  "id": "0708.4387",
  "version": "v1",
  "published": "2007-08-31T16:26:57.000Z",
  "updated": "2007-08-31T16:26:57.000Z",
  "title": "Conjugates of characteristic Sturmian words generated by morphisms",
  "authors": [
    "Amy Glen"
  ],
  "comment": "11 pages",
  "journal": "European Journal of Combinatorics 25 (2004) 1025-1037",
  "doi": "10.1016/j.ejc.2003.12.012",
  "categories": [
    "math.CO",
    "cs.DM"
  ],
  "abstract": "This article is concerned with characteristic Sturmian words of slope $\\alpha$ and $1-\\alpha$ (denoted by $c_\\alpha$ and $c_{1-\\alpha}$ respectively), where $\\alpha \\in (0,1)$ is an irrational number such that $\\alpha = [0;1+d_1,\\bar{d_2,...,d_n}]$ with $d_n \\geq d_1 \\geq 1$. It is known that both $c_\\alpha$ and $c_{1-\\alpha}$ are fixed points of non-trivial (standard) morphisms $\\sigma$ and $\\hat{\\sigma}$, respectively, if and only if $\\alpha$ has a continued fraction expansion as above. Accordingly, such words $c_\\alpha$ and $c_{1-\\alpha}$ are generated by the respective morphisms $\\sigma$ and $\\hat{\\sigma}$. For the particular case when $\\alpha = [0;2,\\bar{r}]$ ($r\\geq1$), we give a decomposition of each conjugate of $c_\\alpha$ (and hence $c_{1-\\alpha}$) into generalized adjoining singular words, by considering conjugates of powers of the standard morphism $\\sigma$ by which it is generated. This extends a recent result of Lev\\'{e} and S\\ee bold on conjugates of the infinite Fibonacci word.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-08-31T16:26:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "68R15",
      "11A55"
    ],
    "keywords": [
      "characteristic sturmian words",
      "infinite fibonacci word",
      "irrational number",
      "standard morphism",
      "generalized adjoining singular words"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0708.4387G"
    }
  }
}