Author:
Allouche Jean-Paul,Currie James,Shallit Jeffrey
Abstract
Let $\overline{\bf t}$ be the infinite fixed point, starting with $1$, of the morphism $\mu: 0 \rightarrow 01$, $1 \rightarrow 10$. An infinite word over $\lbrace 0, 1 \rbrace$ is said to be overlap-free if it contains no factor of the form $axaxa$, where $a \in \lbrace 0,1 \rbrace$ and $x \in \lbrace 0,1 \rbrace^*$. 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 $\overline{\bf t}$. In particular, the lexicographically least infinite overlap-free binary word is $001001 \overline{\bf t}$.
Publisher
The Electronic Journal of Combinatorics
Subject
Computational Theory and Mathematics,Geometry and Topology,Theoretical Computer Science,Applied Mathematics,Discrete Mathematics and Combinatorics
Cited by
15 articles.
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