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 $\alpha$. |
Return to index.
last update: 27.9.2007, webmaster: Petr Ambrož