Shurmian morphisms and α-words

In this paper we prove that the set W of alpha-words over {0, 1} coincides with the set of images of 0 under Sturmian morphisms. This gives an alternative approach of generating alpha-words. For each w is an element of W, a Sturmian solution H of the equation w = H(0) which is a composition of Sturmian morphisms of special forms can be constucted explicitly. In order to demonstrate how results on Sturmian morphic images are reformulated as results on alpha-words and vice versa, we give a Sturmian proof for the conjugation and reversion theorem of alpha-words obtained by the present author in an earlier paper. (C) 1999 Elsevier Science B.V. All rights reserved.