%0 Journal Article
%T Infinite special branches in words associated with beta-expansions
%A Christiane Frougny
%A Zuzana Mas¨¢kov¨¢
%A Edita Pelantov¨¢
%J Discrete Mathematics & Theoretical Computer Science
%D 2007
%I Discrete Mathematics & Theoretical Computer Science
%X A Parry number is a real number ¦Â >1 such that the R¨¦nyi ¦Â-expansion of 1 is finite or infinite eventually periodic. If this expansion is finite, ¦Â is said to be a simple Parry number. Remind that any Pisot number is a Parry number. In a previous work we have determined the complexity of the fixed point u ¦Â of the canonical substitution associated with ¦Â-expansions, when ¦Â is a simple Parry number. In this paper we consider the case where ¦Â is a non-simple Parry number. We determine the structure of infinite left special branches, which are an important tool for the computation of the complexity of u ¦Â. These results allow in particular to obtain the following characterization: the infinite word u ¦Â is Sturmian if and only if ¦Â is a quadratic Pisot unit.
%U http://www.dmtcs.org/dmtcs-ojs/index.php/dmtcs/article/view/658