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Following Inoue et al., we define a word to be a repetition if it is a (fractional) power of exponent at least Formula: see text. 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.
Rampersad et al. (Tue,) studied this question.