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Abelian Repetitions in Sturmian Words
[chapter]

2013
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Lecture Notes in Computer Science
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We investigate abelian repetitions in Sturmian words. We exploit a bijection between factors of Sturmian words and subintervals of the unitary segment that allows us to study the periods of abelian repetitions by using classical results of elementary Number Theory. If km denotes the maximal exponent of an abelian repetition of period m, we prove that lim sup km/m ≥ √ 5 for any Sturmian word, and the equality holds for the Fibonacci infinite word. We further prove that the longest prefix of the

doi:10.1007/978-3-642-38771-5_21
fatcat:u7br3sk5mba5bcymopm3lzezzy