LARGE SIMPLE BINARY EQUALITY WORDS
Let two nonperiodic binary morphisms g, h : {a,b}* -> Delta* be given. A word w is called a solution of q and h if g(w)= h(w). We say that a solution w is simple if whenever w(1), w(1)u, w(2) and w(2)u' are prefixes of w(omega) such that g(w(1))z = h(w(2)), and g(w(1)u)z = h(w(2)u') for some word z, then vertical bar mu vertical bar = vertical bar mu'vertical bar = k vertical bar w vertical bar, for some k is an element of 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)(i)a, or w - a(j)b(k) with gcd(j, k) - 1, up to the exchange of letters a and b.
combinatorics on words equality set post correspondence problem