Binary words avoiding the pattern AABBCABBA

Pascal Ochem

RAIRO - Theoretical Informatics and Applications (2010)

  • Volume: 44, Issue: 1, page 151-158
  • ISSN: 0988-3754

Abstract

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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 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.

How to cite

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Ochem, 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

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  7. P. Ochem, A generator of morphisms for infinite words. RAIRO-Theor. Inf. Appl.40 (2006) 427–441.  Zbl1110.68122
  8. P. Ochem, Letter frequency in infinite repetition-free words. Theoret. Comput. Sci.380 (2007) 388–392.  Zbl1115.68124
  9. 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/
  10. A.M. Shur, Combinatorial complexity of regular languages. CSR 2008. Lect. Notes Comput. Sci.5010 (2008) 289–301.  Zbl1142.68428
  11. A.I. Zimin, Blocking sets of terms. Math. USSR Sbornik47 (1984) 353–364. English translation.  Zbl0599.20106

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