Combinatorical and Algebraic Structures Seminar

Session details

Date: 23.4.2013
Speaker: Christiane Frougny, LIAFA, Université Paris VII
Title: Sturmian graphs and integer representations over numeration systems
Abstract: (spoluautoři: C. Epifanio, A. Gabriele, F. Mignosi and J. Shallit)
In this work we consider a numeration system, originally due to Ostrowski, based on the continued fraction expansion of a real number $\alpha$. We show that the set of lazy representations of the natural integers in this numeration system is regular if and only if the continued fraction expansion of $\alpha$ is eventually periodic. The main result of the paper is that for any number $i$ the unique path weighted $i$ in the Sturmian graph associated with $\alpha$ represents the lazy representation of $i$ in the Ostrowski numeration system associated with $\alpha$.

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