The number of binary rotation words
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Volume 48 (2014) no. 4, pp. 453-465.

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.

DOI: 10.1051/ita/2014019
Classification: 68R15,  37B10
Keywords: rotation, rotation words, Sturmian words, subword complexity, total complexity
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     title = {The number of binary rotation words},
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Frid, A.; Jamet, D. The number of binary rotation words. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Volume 48 (2014) no. 4, pp. 453-465. doi : 10.1051/ita/2014019. http://www.numdam.org/articles/10.1051/ita/2014019/

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