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2021 A gap of the exponents of repetitions of Sturmian words
Suzue Ohnaka, Takao Watanabe
Mosc. J. Comb. Number Theory 10(3): 203-234 (2021). DOI: 10.2140/moscow.2021.10.203

Abstract

By measuring second occurring times of factors of an infinite word x, Bugeaud and Kim introduced a new quantity rep(x) called the exponent of repetition of x. It was proved by Bugeaud and Kim that 1 rep(x)rmax=1032 if x is a Sturmian word. We determine the value r1 such that there is no Sturmian word x satisfying r1< rep(x)<rmax and r1 is an accumulation point of the set of rep(x) when x runs over the Sturmian words.

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Suzue Ohnaka. Takao Watanabe. "A gap of the exponents of repetitions of Sturmian words." Mosc. J. Comb. Number Theory 10 (3) 203 - 234, 2021. https://doi.org/10.2140/moscow.2021.10.203

Information

Received: 9 January 2021; Revised: 18 May 2021; Accepted: 7 June 2021; Published: 2021
First available in Project Euclid: 15 November 2021

Digital Object Identifier: 10.2140/moscow.2021.10.203

Subjects:
Primary: 68R15
Secondary: 11A55 , 11A63

Keywords: combinatorics on words , Continued fraction , Irrationality exponent , irrationality measure , Sturmian word

Rights: Copyright © 2021 Mathematical Sciences Publishers

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Vol.10 • No. 3 • 2021
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