Sturmian morphisms and α-words

AbstractIn this paper we prove that the set W of α-words over {0,1} coincides with the set of images of 0 under Sturmian morphisms. This gives an alternative approach of generating α-words. For each w ϵ W, a Sturmian solution H of the equation w = H(0) which is a composition of Sturmian morphisms of special forms can be constructed explicitly. In order to demonstrate how results on Sturmian morphic images are reformulated as results on α-words and vice versa, we give a Sturmian proof for the conjugation and reversion theorem of α-words obtained by the present author in an earlier paper