Extremal infinite overlap-free binary words
type: Item
instance of: scholarly article
title: Extremal infinite overlap-free binary words
zbMATH Open document ID: 0890.68107
published in: The Electronic Journal of Combinatorics
publication date: 1998-05-24T00:00:00Z
full work available at URL: https://eudml.org/doc/119482
full work available at URL: v5i1r27.html
review text: 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 \(001001 \overline{\mathbf t}\).
Mathematics Subject Classification ID: 68R15
zbMATH DE Number: 1154471
zbMATH Keywords: overlap-free
zbMATH Keywords: binary word
author: Jean-Paul Allouche
author: James D. Currie
author: Jeffrey Shallit
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1154471