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Binary words avoiding the pattern AABBCABBA

Published online by Cambridge University Press:  11 February 2010

Pascal Ochem
Pascal Ochem*
Affiliation:
CNRS, Lab. J.V. Poncelet, Moscow; [email protected] LRI, Bât 490 Université Paris-Sud 11, 91405 Orsay Cedex, France.
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Abstract

We show that there are three types of infinite words over the two-letter alphabet {0,1} that avoid the pattern AABBCABBA. These types, P, E0, and E1, differ by the factor complexity and the asymptotic frequency of the letter 0. Type P has polynomial factor complexity and letter frequency $\frac{1}{2}$. Type E0 has exponential factor complexity and the frequency of the letter 0 is at least 0.45622 and at most 0.48684. Type E1 is obtained from type E0 by exchanging 0 and 1.

Keywords

Combinatorics on wordsletter frequencyfactor complexity
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 44 , Issue 1: Special issue dedicated to the 12th "Journées Montoises d'Informatique Théorique" , January 2010 , pp. 151 - 158
Copyright
© EDP Sciences, 2010

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