The Block Structure of Successor Morphisms

Abstract

Let g ₁,h ₁: {a,b}^* → {a,b}^* be successor morphisms of non-periodic binary morphisms g,h. Suppose that g,h have a minimal solution which is not simple. Let (e,f),(e′,f′) be letter blocks of g ₁,h ₁, that is, a prefix minimal pairs of words such that g ₁(e) = h ₁(f) and g ₁(e′) = h ₁(f′). In this paper we will show that if the primitive roots of words {g ₁(a), g ₁(b), h ₁(a), h ₁(b), e, f, e′, f′} have the length at least two, then the length of both letter blocks (e,f), (e′,f′) is bounded by a constant.