The subword complexity of fixed points of binary uniform morphisms

Abstract

We obtain a formula for the subword complexity of every binary DOL word which is a fixed point of a uniform morphism, i.e. a morphism in which the images of all letters have the same length. We establish that the complexity function can be found from its values for little lengths and some simple parameters of the morphism. The property of circularity is important for the view of the formula. In general case the subword complexity function has much the same behavour as the complexity function of the Thue-Morse word.