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The number of binary rotation words∗

Published online by Cambridge University Press:  11 August 2014

A. Frid  and
D. Jamet
A. Frid
Affiliation:
Sobolev Institute of Mathematics SB RAS, Koptyug Av. 4, 630090, Novosibirsk, Russia, and Université de Lorraine, 34 cours Léopold, CS 25233, 54052 Nancy cedex, France.. anna.e.frid@gmail.com
D. Jamet
Affiliation:
LORIA, UMR 7503, Campus scientifique BP 239, 54506 Vandoeuvre-lès-Nancy cedex, France.
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Abstract

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.

Keywords

Rotationrotation wordsSturmian wordssubword complexitytotal complexity

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