Construction of a bi-infinite power free word with a given factor and a non-recurrent letter

Abstract

Let $L_{k,\alpha }^{\mathbb{Z}}$ denote the set of all bi-infinite $\alpha$-power free words over an alphabet with $k$ letters, where $\alpha$ is a positive rational number and $k$ is positive integer. We prove that if $\alpha \ge 5$, $k\ge 3$, $v\in L_{k,\alpha }^{\mathbb{Z}}$, and $w$ is a finite factor of $v$, then there are $\tilde{v}\in L_{k,\alpha }^{\mathbb{Z}}$ and a letter $x$ such that $w$ is a factor of $\tilde{v}$ and $x$ has only a finitely many occurrences in $\tilde{v}$.

References in corpus (2)

• Subword complexity and power avoidance
• Transition Property for $\alpha$-Power Free Languages with $\alpha \ge 2$ and $k\ge 3$ Letters