2-balanced sequences coding rectangle exchange transformation

Abstract

We define a new class of ternary sequences that are 2-balanced. These sequencesare obtained by colouring of Sturmian sequences. We show that the class containssequences of any given letter frequencies. We provide an upper bound on factorand abelian complexity of these sequences. Using the interpretation by rectangleexchange transformation, we prove that for almost all triples of letter frequencies,the upper bound on factor and abelian complexity is reached. The bound onfactor complexity is given using a number-theoretical function which we computeexplicitly for a class of parameters. MSC Classification: 68R15