Extremal infinite overlap-free binary words
Summary: Let \(\overline{\mathbf t}\) be the infinite fixed point, starting with \(1\), of the morphism \(\mu: 0 \rightarrow 01\), \(1 \rightarrow 10\). An infinite word over \(\{ 0, 1 \}\) is said to be overlap-free if it contains no factor of the form \(axaxa\), where \(a \in \{ 0,1 \}\) and \(x \in \{ 0,1 \}^*\). We prove that the lexicographically least infinite overlap-free binary word beginning with any specified prefix, if it exists, has a suffix which is a suffix of \ \(\overline{\mathbf t}\). In particular, the lexicographically least infinite overlap-free binary word is \(001001 \overline{\mathbf t}\).
scientific article; zbMATH DE number 1154471