Recent Results In Sturmian Words
Jean Berstel · 1995
In this survey paper, we present some recent results concerning finite and infinite Sturmian words. We emphasize on the different definitions of Sturmian words, and various subclasses, and give the ways to construct them related to continued fraction expansion. Next, we give properties of special finite Sturmian words, called standard words. Among these, a decomposition into palindromes, a relation with the periodicity theorem of Fine and Wilf, and the fact that all these words are Lyndon words. Finally, we describe the structure of Sturmian morphisms (i.e. morphisms that preserve Sturmian words) which is now rather well understood. 1 Introduction Combinatorial properties of finite and infinite words are of increasing importance in various fields of physics, biology, mathematics and computer science. Infinite words generated by various devices have been considered [9]. We are interested here in a special family of infinite words, namely Sturmian words. Sturmian words represent...