Geodesic
A length bound for binary equality words
Commentationes Mathematicae Universitatis Carolinae, Tome 52 (2011) no. 1, pp. 1-20

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Let $w$ be an equality word of two binary non-periodic morphisms $g,h: \{a,b\}^* \to \Delta^*$ with unique overflows. It is known that if $w$ contains at least 25 occurrences of each of the letters $a$ and $b$, then it has to have one of the following special forms: up to the exchange of the letters $a$ and $b$ either $w=(ab)^ia$, or $w=a^ib^j$ with $\operatorname{gcd} (i,j)=1$. We will generalize the result, justify this bound and prove that it can be lowered to nine occurrences of each of the letters $a$ and $b$.
Classification : 68R15
Keywords: combinatorics on words; binary equality languages 
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Hadravová, Jana. A length bound for binary equality words. Commentationes Mathematicae Universitatis Carolinae, Tome 52 (2011) no. 1, pp. 1-20. http://geodesic.mathdoc.fr/item/CMUC_2011__52_1_a0/