论文标题
斯特里亚语单词重复指数的差距
A gap of the exponents of repetitions of Sturmian words
论文作者
论文摘要
通过测量无限单词$ x $的第二个发生时间，Bugeaud和Kim引入了一个新数量$ {\ rm rep}（x）$，称为$ x $的重复的指数。 bugeaud和kim证明了$ 1 \ leq {\ rm rep}（x）\ leq r _ {\ max} = \ sqrt {10} -3/2 $如果$ x $是sturmian单词。在本文中，我们确定$ r_1 $的值，使得没有Sturmian单词$ x $满足$ r_1 <{\ rm rep}（x）<r _ {\ max} $，$ r_1 $是$ {\ rm rep}（x）$ cul the sturmian单词的$ {\ rm rep} $的集合点。
By measuring second occurring times of factors of an infinite word $x$, Bugeaud and Kim introduced a new quantity ${\rm rep}(x)$ called the exponent of repetition of $x$. It was proved by Bugeaud and Kim that $1 \leq {\rm rep}(x) \leq r_{\max} = \sqrt{10} - 3/2$ if $x$ is a Sturmian words. In this paper, we determine the value $r_1$ such that there is no Sturmian word $x$ satisfying $r_1 < {\rm rep}(x) < r_{\max}$ and $r_1$ is an accumulation point of the set of ${\rm rep}(x)$ when $x$ runs over the Sturmian words.
