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A length bound for binary equality words

Jana Hadravová — 2011

Commentationes Mathematicae Universitatis Carolinae

Let $w$ be an equality word of two binary non-periodic morphisms $g, h : {a, b}^{*} \to Δ^{*}$ 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 $w = {(a b)}^{i} a$ , or $w = a^{i} b^{j}$ with $gcd (i, j) = 1$ . 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 $b$ .

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