### Abstract

Lingua originale | English |
---|---|

pagine (da-a) | 1014-1030 |

Numero di pagine | 17 |

Rivista | Discrete Applied Mathematics |

Volume | 155 |

Stato di pubblicazione | Published - 2007 |

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### All Science Journal Classification (ASJC) codes

- Discrete Mathematics and Combinatorics
- Applied Mathematics

### Cita questo

*Discrete Applied Mathematics*,

*155*, 1014-1030.

**On Sturmian Graphs.** / Mignosi, Filippo; Epifanio, Chiara; Venturini, Ilaria; Mignosi, Filippo; Shallit, Jeffrey.

Risultato della ricerca: Article

*Discrete Applied Mathematics*, vol. 155, pagg. 1014-1030.

}

TY - JOUR

T1 - On Sturmian Graphs

AU - Mignosi, Filippo

AU - Epifanio, Chiara

AU - Venturini, Ilaria

AU - Mignosi, Filippo

AU - Shallit, Jeffrey

PY - 2007

Y1 - 2007

N2 - In this paper we define Sturmian graphs and we prove that all of them have a certain ''''counting'''' property. We show deep connections between this counting property and two conjectures, by Moser and by Zaremba, on the continued fraction expansion of real numbers. These graphs turn out to be the underlying graphs of compact directed acyclic word graphs of central Sturmian words. In order to prove this result, we give a characterization of the maximal repeats of central Sturmian words. We show also that, in analogy with the case of Sturmian words, these graphs converge to infinite ones.

AB - In this paper we define Sturmian graphs and we prove that all of them have a certain ''''counting'''' property. We show deep connections between this counting property and two conjectures, by Moser and by Zaremba, on the continued fraction expansion of real numbers. These graphs turn out to be the underlying graphs of compact directed acyclic word graphs of central Sturmian words. In order to prove this result, we give a characterization of the maximal repeats of central Sturmian words. We show also that, in analogy with the case of Sturmian words, these graphs converge to infinite ones.

UR - http://hdl.handle.net/10447/14526

M3 - Article

VL - 155

SP - 1014

EP - 1030

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

SN - 0166-218X

ER -