Sturmian graphs and a conjecture of moser

Authors:
Chiara Epifanio;Filippo Mignosi;Jeffrey Shallit;Ilaria Venturini
Affiliations:
Dip. Mat. e Appl., Univ. di Palermo, Italy;Dip. Mat. e Appl., Univ. di Palermo, Italy;School of Computer Science, University of Waterloo, Ontario, Canada;TSI, ENST, Paris, France
Venue:
DLT'04 Proceedings of the 8th international conference on Developments in Language Theory
Year:
2004

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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.