论文标题
用给定因子和非循环字母的双涉及电源的构建
Construction of a bi-infinite power free word with a given factor and a non-recurrent letter
论文作者
论文摘要
令$ l_ {k，α}^{\ mathbb {z}} $表示所有Bi-Infinite $α$ - $ k $字母上的所有Bi-Infinite $α$ - 供电的单词，其中$α$是一个正理性的数字，$ k $是正整数。我们证明，如果$α\ geq 5 $，$ k \ geq 3 $，$ v \ in l_ {k，α}^{\ mathbb {z}} $，而$ w $是$ v $的有限因子，则有$ \ widetilde v \ in l_ { $ w $是$ \ widetilde v $，$ x $在$ \ widetilde v $中只有有限的发生。
Let $L_{k,α}^{\mathbb{Z}}$ denote the set of all bi-infinite $α$-power free words over an alphabet with $k$ letters, where $α$ is a positive rational number and $k$ is positive integer. We prove that if $α\geq 5$, $k\geq 3$, $v\in L_{k,α}^{\mathbb{Z}}$, and $w$ is a finite factor of $v$, then there are $\widetilde v\in L_{k,α}^{\mathbb{Z}}$ and a letter $x$ such that $w$ is a factor of $\widetilde v$ and $x$ has only a finitely many occurrences in $\widetilde v$.
