On Lazy Representations and Sturmian Graphs

  • Chiara Epifanio
  • Christiane Frougny
  • Alessandra Gabriele
  • Filippo Mignosi
  • Jeffrey Shallit
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6482)

Abstract

In this paper we establish a strong relationship between the set of lazy representations and the set of paths in a Sturmian graph associated with a real number α. We prove that for any non-negative integer i the unique path weighted i in the Sturmian graph associated with α represents the lazy representation of i in the Ostrowski numeration system associated with α. Moreover, we provide several properties of the representations of the natural integers in this numeration system.

Keywords

numeration systems Sturmian graphs continued fractions 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Chiara Epifanio
    • 1
  • Christiane Frougny
    • 2
  • Alessandra Gabriele
    • 1
  • Filippo Mignosi
    • 3
  • Jeffrey Shallit
    • 4
  1. 1.Dipartimento di Matematica e InformaticaUniversità di PalermoItaly
  2. 2.LIAFA, CNRS & Université Paris 7, and Université Paris 8France
  3. 3.Dipartimento di InformaticaUniversità di L’AquilaItaly
  4. 4.School of Computer ScienceUniversity of WaterlooCanada

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