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.
Partially supported by MIUR National Project PRIN “Aspetti matematici e applicazioni emergenti degli automi e dei linguaggi formali”.
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Epifanio, C., Frougny, C., Gabriele, A., Mignosi, F., Shallit, J. (2011). On Lazy Representations and Sturmian Graphs. In: Domaratzki, M., Salomaa, K. (eds) Implementation and Application of Automata. CIAA 2010. Lecture Notes in Computer Science, vol 6482. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18098-9_14
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DOI: https://doi.org/10.1007/978-3-642-18098-9_14
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