On lazy representations and sturmian graphs

Authors:
Chiara Epifanio;Christiane Frougny;Alessandra Gabriele;Filippo Mignosi;Jeffrey Shallit
Affiliations:
Dipartimento di Matematica e Informatica, Università di Palermo, Italy;LIAFA, CNRS & Université Paris 7, and Université Paris 8, France;Dipartimento di Matematica e Informatica, Università di Palermo, Italy;Dipartimento di Informatica, Università di L'Aquila, Italy;School of Computer Science, University of Waterloo, Ontario, Canada
Venue:
CIAA'10 Proceedings of the 15th international conference on Implementation and application of automata
Year:
2010

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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.