关于三个区间交换变换中幂的注记
Note on powers in three interval exchange transformations
摘要：
本文研究了无限字编码交换中的重复问题，即三个具有（3，2，1）排列的区间，称之为3iet字。这些单词的语言由两个参数$\varepsilon,\ell$确定。我们证明了3iet字的索引的有限性等价于$\varepsilon$的连分数的系数的有界性。在这种情况下，我们也给出了相应的3iet字的索引的上下估计。
英文摘要：
We study repetitions in infinite words coding exchange of three intervals with permutation (3,2,1), called 3iet words. The language of such words is determined by two parameters $\varepsilon,\ell$. We show that finiteness of the index of 3iet words is equivalent to boundedness of the coefficients of the continued fraction of $\varepsilon$. In this case we also give an upper and lower estimate on the index of the corresponding 3iet word.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
