Subword complexity and power avoidance

01/16/2018

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by   Jeffrey Shallit, et al.

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We begin a systematic study of the relations between subword complexity of infinite words and their power avoidance. Among other things, we show that -- the Thue-Morse word has the minimum possible subword complexity over all overlap-free binary words and all (7/3)-power-free binary words, but not over all (7/3)^+-power-free binary words; -- the twisted Thue-Morse word has the maximum possible subword complexity over all overlap-free binary words, but no word has the maximum subword complexity over all (7/3)-power-free binary words; -- if some word attains the minimum possible subword complexity over all square-free ternary words, then one such word is the ternary Thue word; -- the recently constructed 1-2-bonacci word has the minimum possible subword complexity over all symmetric square-free ternary words.