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Initial non-repetitive complexity of infinite words (1507.08206v3)
Published 29 Jul 2015 in math.CO and cs.FL
Abstract: The initial non-repetitive complexity function of an infinite word x (first defined by Moothathu) is the function of n that counts the number of distinct factors of length n that appear at the beginning of x prior to the first repetition of a length-n factor. We examine general properties of the initial non-repetitive complexity function, as well as obtain formulas for the initial non-repetitive complexity of the Thue-Morse word, the Fibonacci word and the Tribonacci word.