## Jana Hadravová

*A length bound for binary equality words*

Comment.Math.Univ.Carolin. 52,1 (2011) 1-20.**Abstract:**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~$b$.

**Keywords:** combinatorics on words, binary equality languages

**AMS Subject Classification:** 68R15

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