LARGE SIMPLE BINARY EQUALITY WORDS

Abstract

Let two nonperiodic binary morphisms g,h: {a,b}* → Δ* be given. A word w is called a solution of g and h if g(w)=h(w). We say that a solution w is simple if whenever w1, w1u, w2and w2u' are prefixes of wωsuch that [Formula: see text] for some word z, then |u|=|u'|=k|w|, for some k ∈ ℕ. In this paper we will study simple solutions and show that if a word w is a simple solution containing at least nine occurrences of the letter a and at least nine occurrences of the letter b, then either w=(ab)ia, or w=ajbkwith gcd (j, k) = 1, up to the exchange of letters a and b.