论文标题
重复的特征性sturmian单词的指数，其斜率是二次不合理的
The exponent of repetition of the characteristic Sturmian word whose slope is a quadratic irrational
论文作者
论文摘要
对于一个无限的单词$ x $，Bugeaud和Kim引入了一个数量$ \ mathrm {rep}（x）$，称为$ x $重复的指数。我们证明$ \ mathrm {rep}（x）= \ mathrm {rep}（y）$持有sturmian word $ x $和每个后缀$ y $的$ x $。令$ c $为斜率$θ$的特征性sturmian单词。当$θ$是二次非理性时，给出了$ \ mathrm {rep}（c）$的公式。此公式表明，如果$ \ mathrm {rep}（c）= \ mathrm {rep}（c'）$如果$ c'$是特征性的sturmian单词，其斜率是二次非理性的，等于$θ$。
For an infinite word $x$, Bugeaud and Kim introduced a quantity $\mathrm{rep}(x)$ called the exponent of repetition of $x$. We prove that $\mathrm{rep}(x) = \mathrm{rep}(y)$ holds for a Sturmian word $x$ and every suffix $y$ of $x$. Let $c$ be the characteristic Sturmian word of slope $θ$. When $θ$ is a quadratic irrational, a formula of $\mathrm{rep}(c)$ is given. This formula shows that $\mathrm{rep}(c) = \mathrm{rep}(c')$ if $c'$ is the characteristic Sturmian word whose slope is a quadratic irrational equivalent to $θ$.
