Abstract
In this paper we define Sturmian graphs and we prove that all of them have a “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 CDAWGs of central Sturmian words. We show also that, analogously to the case of Sturmian words, these graphs converge to infinite ones.
Partially supported by MIUR National Project PRIN “Linguaggi Formali e Automi: teoria ed applicazioni.”
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Epifanio, C., Mignosi, F., Shallit, J., Venturini, I. (2004). Sturmian Graphs and a Conjecture of Moser. In: Calude, C.S., Calude, E., Dinneen, M.J. (eds) Developments in Language Theory. DLT 2004. Lecture Notes in Computer Science, vol 3340. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30550-7_15
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DOI: https://doi.org/10.1007/978-3-540-30550-7_15
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