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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; ochem@lri.fr 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-letteralphabet {0,1} that avoid the pattern AABBCABBA. These types, P, E 0, and E 1,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 E 0 has exponential factor complexity and the frequency of the letter 0 is at least0.45622 and at most 0.48684. Type E 1 is obtained from type E 0 by exchanging 0 and 1.

Keywords

Combinatorics on wordsletter frequencyfactor complexity

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