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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 . 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.
@article{ITA_2010__44_1_151_0,
author = {Ochem, Pascal},
title = {Binary words avoiding the pattern {AABBCABBA}},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
pages = {151--158},
publisher = {EDP-Sciences},
volume = {44},
number = {1},
year = {2010},
doi = {10.1051/ita/2010010},
mrnumber = {2604940},
zbl = {1184.68377},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/ita/2010010/}
}
TY - JOUR AU - Ochem, Pascal TI - Binary words avoiding the pattern AABBCABBA JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications PY - 2010 SP - 151 EP - 158 VL - 44 IS - 1 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/ita/2010010/ DO - 10.1051/ita/2010010 LA - en ID - ITA_2010__44_1_151_0 ER -
%0 Journal Article %A Ochem, Pascal %T Binary words avoiding the pattern AABBCABBA %J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications %D 2010 %P 151-158 %V 44 %N 1 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/ita/2010010/ %R 10.1051/ita/2010010 %G en %F ITA_2010__44_1_151_0
Ochem, Pascal. Binary words avoiding the pattern AABBCABBA. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 44 (2010) no. 1, pp. 151-158. doi: 10.1051/ita/2010010
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