Following Inoue et al., we define a word to be a repetition if it is a (fractional) power of exponent at least 2. A word has a repetition factorization if it is the product of repetitions. We study repetition factorizations in several (generalized) automatic sequences, including the infinite Fibonacci word, the Thue-Morse word, paperfolding words, and the Rudin-Shapiro sequence.
翻译:继Inoue等人之后,我们将单词定义为重复,如果它是指数至少为2的(分数)幂。如果一个单词是重复的乘积,则它具有重复因子分解。我们研究了若干(广义)自动序列中的重复因子分解,包括无限Fibonacci词、Thue-Morse词、折纸词和Rudin-Shapiro序列。