Hostname: page-component-cb9f654ff-hn9fh Total loading time: 0 Render date: 2025-08-24T00:02:33.954Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Baker, K.A., McNulty, G.F. and Taylor, W., Growth problems for avoidable words. Theoret. Comput. Sci. 69 (1989) 319–345. CrossRef
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). http://www-igm.univ-mlv.fr/ berstel/Articles/1994ThueTranslation.pdf
Berstel, J., Growth of repetition-free words - a review. Theoret. Comput. Sci. 340 (2005) 280–290. CrossRef
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 Sequences 10 (2007) Article 07.3.2.
Ochem, P., A generator of morphisms for infinite words. RAIRO-Theor. Inf. Appl. 40 (2006) 427–441. CrossRef
Ochem, P., Letter frequency in infinite repetition-free words. Theoret. Comput. Sci. 380 (2007) 388–392. CrossRef
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). http://www.lri.fr/ ochem/morphisms/wowa.ps
Shur, A.M., Combinatorial complexity of regular languages. CSR 2008. Lect. Notes Comput. Sci. 5010 (2008) 289–301. CrossRef
Zimin, A.I., Blocking sets of terms. Math. USSR Sbornik 47 (1984) 353–364. English translation. CrossRef