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.
Epifanio, C., Frougny, C., Gabriele, A., Mignosi, F., Shallit, J. (2011). On lazy representations and Sturmian graphs. In K.S. M. Domaratzki (a cura di), 15th International Conference, CIAA 2010 (pp. 125-134) [10.1007/978-3-642-18098-9_14].
On lazy representations and Sturmian graphs
EPIFANIO, Chiara;
2011-01-01
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.
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