Binary words avoiding the pattern AABBCABBA
RAIRO - Theoretical Informatics and Applications (2010)
- Volume: 44, Issue: 1, page 151-158
- ISSN: 0988-3754
Access Full Article
top
Abstract
topHow to cite
topOchem, Pascal. "Binary words avoiding the pattern AABBCABBA." RAIRO - Theoretical Informatics and Applications 44.1 (2010): 151-158. <http://eudml.org/doc/250803>.
@article{Ochem2010,
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.
},
author = {Ochem, Pascal},
journal = {RAIRO - Theoretical Informatics and Applications},
keywords = {Combinatorics on words; letter frequency; factor complexity; combinatorics on words},
language = {eng},
month = {2},
number = {1},
pages = {151-158},
publisher = {EDP Sciences},
title = {Binary words avoiding the pattern AABBCABBA},
url = {http://eudml.org/doc/250803},
volume = {44},
year = {2010},
}
TY - JOUR
AU - Ochem, Pascal
TI - Binary words avoiding the pattern AABBCABBA
JO - RAIRO - Theoretical Informatics and Applications
DA - 2010/2//
PB - EDP Sciences
VL - 44
IS - 1
SP - 151
EP - 158
AB -
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.
LA - eng
KW - Combinatorics on words; letter frequency; factor complexity; combinatorics on words
UR - http://eudml.org/doc/250803
ER -
References
top- K.A. Baker, G.F. McNulty and W. Taylor, Growth problems for avoidable words. Theoret. Comput. Sci.69 (1989) 319–345.
- J. Berstel, Axel Thue's papers on repetitions in words: a translation. Publications du LaCIM, Département de mathématiques et d'informatique 95, Université du Québec à Montréal (1995). berstel/Articles/1994ThueTranslation.pdf URIhttp://www-igm.univ-mlv.fr/
- J. Berstel, Growth of repetition-free words - a review. Theoret. Comput. Sci.340 (2005) 280–290.
- J. Cassaigne, Motifs évitables et régularité dans les mots. Thèse de Doctorat, Université Paris VI (1994).
- R.J. Clark, Avoidable formulas in combinatorics on words. Ph.D. thesis, University of California, Los Angeles (2001).
- R. Kolpakov, Efficient lower bounds on the number of repetition-free words. J. Integer Sequences10 (2007) Article 07.3.2.
- P. Ochem, A generator of morphisms for infinite words. RAIRO-Theor. Inf. Appl.40 (2006) 427–441.
- P. Ochem, Letter frequency in infinite repetition-free words. Theoret. Comput. Sci.380 (2007) 388–392.
- P. Ochem and T. Reix, Upper bound on the number of ternary square-free words, Proceedings of the Workshop on Words and Automata (WOWA'06) (St Petersburg, June 2006). ochem/morphisms/wowa.ps URIhttp://www.lri.fr/
- A.M. Shur, Combinatorial complexity of regular languages. CSR 2008. Lect. Notes Comput. Sci.5010 (2008) 289–301.
- A.I. Zimin, Blocking sets of terms. Math. USSR Sbornik47 (1984) 353–364. English translation.
Citations in EuDML Documents
topNotesEmbed ?
topYou must be logged in to post comments.
To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.