On Sturmian Graphs

Chiara Epifanio, Filippo Mignosi, Ilaria Venturini, Filippo Mignosi, Jeffrey Shallit

Risultato della ricerca: Articlepeer review

6 Citazioni (Scopus)

Abstract

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.
Lingua originaleEnglish
pagine (da-a)1014-1030
Numero di pagine17
RivistaDiscrete Applied Mathematics
Volume155
Stato di pubblicazionePublished - 2007

All Science Journal Classification (ASJC) codes

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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