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Sturmian graphs and a conjecture of Moser. (English) Zbl 1117.68454
Calude, Cristian S. (ed.) et al., Developments in language theory. 8th international conference, DLT 2004, Auckland, New Zealand, December 13–17, 2004. Proceedings. Berlin: Springer (ISBN 3-540-24014-4/pbk). Lecture Notes in Computer Science 3340, 175-187 (2004).
Summary: 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.
MSC:
68R10Graph theory in connection with computer science (including graph drawing)
68R15Combinatorics on words
05C75Structural characterization of families of graphs