Initial non-repetitive complexity of infinite words
Jeremy Nicholson, Narad Rampersad
TL;DR
This paper studies the initial non-repetitive complexity of infinite words, analyzing its properties and deriving formulas for specific well-known sequences like Thue-Morse, Fibonacci, and Tribonacci words.
Contribution
It introduces and explores the initial non-repetitive complexity function, providing formulas for key infinite words and enhancing understanding of their early factor structure.
Findings
Formulas for initial non-repetitive complexity of Thue-Morse, Fibonacci, and Tribonacci words
Properties of the initial non-repetitive complexity function
Insights into early factor repetitions in infinite words
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.
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