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rotation words

RAIRO - Theoretical Informatics and Applications (1)

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The number of binary rotation words ∗
A. Frid, D. Jamet
Journal:

RAIRO - Theoretical Informatics and Applications / Volume 48 / Issue 4 / October 2014

Published online by Cambridge University Press:

11 August 2014, pp. 453-465

Print publication:

October 2014
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We consider binary rotation words generated by partitions of the unit circle to two intervals and give a precise formula for the number of such words of length n. We also give the precise asymptotics for it, which happens to be Θ(n4). The result continues the line initiated by the formula for the number of all Sturmian words obtained by Lipatov [Problemy Kibernet. 39 (1982) 67–84], then independently by Mignosi [Theoret. Comput. Sci. 82 (1991) 71–84], and others.