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Sturmian Graphs and a Conjecture of Moser

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Developments in Language Theory (DLT 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3340))

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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.

Partially supported by MIUR National Project PRIN “Linguaggi Formali e Automi: teoria ed applicazioni.”

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Author information

Authors and Affiliations

  1. Dip. Mat. e Appl., Univ. di Palermo, Italy

    Chiara Epifanio & Filippo Mignosi

  2. School of Computer Science, University of Waterloo, Ontario, Canada

    Jeffrey Shallit

  3. TSI, ENST, Paris, France

    Ilaria Venturini

Authors
  1. Chiara Epifanio
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  2. Filippo Mignosi
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  3. Jeffrey Shallit
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  4. Ilaria Venturini
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Auckland, New Zealand

    Cristian S. Calude

  2. Computer Science, Institute of Information and Mathematical Sciences, Massey University Albany, Auckland, New Zealand

    Elena Calude

  3. Department of Computer Science, University of Auckland, Private Bag 92019, Auckland, New Zealand

    Michael J. Dinneen

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© 2004 Springer-Verlag Berlin Heidelberg

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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

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-24014-3

  • Online ISBN: 978-3-540-30550-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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