Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
420969 | Discrete Applied Mathematics | 2007 | 17 Pages |
Abstract
In this paper we define Sturmian graphs and we prove that all of them have a certain “counting” property. We show deep connections between this counting property and two conjectures, by Moser and by Zaremba, on the continued fraction expansion of real numbers. These graphs turn out to be the underlying graphs of compact directed acyclic word graphs of central Sturmian words. In order to prove this result, we give a characterization of the maximal repeats of central Sturmian words. We show also that, in analogy with the case of Sturmian words, these graphs converge to infinite ones.
Related Topics
Physical Sciences and Engineering
Computer Science
Computational Theory and Mathematics
Authors
Chiara Epifanio, Filippo Mignosi, Jeffrey Shallit, Ilaria Venturini,