On avoidability of formulas with reversal

Leroy, J. ;  Rigo, M. ;  Charlier, E. (éd.)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Special issue dedicated to the 16th "Journées Montoises d’Informatique Théorique", Tome 51 (2017) no. 4, pp. 181-189.

While a characterization of unavoidable formulas (without reversal) is well-known, little is known about the avoidability of formulas with reversal in general. In this article, we characterize the unavoidable formulas with reversal that have at most two one-way variables (x is a one-way variable in formula with reversal ϕ if exactly one of x and xR appears in ϕ).

Accepté le :
DOI : 10.1051/ita/2017013
Classification : 68R15
Mots-clés : Pattern avoidance, formula with reversal, unavoidability
Currie, James D. 1 ; Mol, Lucas 1 ; Rampersad, Narad 1

1 
@article{ITA_2017__51_4_181_0,
     author = {Currie, James D. and Mol, Lucas and Rampersad, Narad},
     editor = {Leroy, J. and Rigo, M. and Charlier, E.},
     title = {On avoidability of formulas with reversal},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {181--189},
     publisher = {EDP-Sciences},
     volume = {51},
     number = {4},
     year = {2017},
     doi = {10.1051/ita/2017013},
     mrnumber = {3782819},
     zbl = {1390.68512},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/ita/2017013/}
}
TY  - JOUR
AU  - Currie, James D.
AU  - Mol, Lucas
AU  - Rampersad, Narad
ED  - Leroy, J.
ED  - Rigo, M.
ED  - Charlier, E.
TI  - On avoidability of formulas with reversal
JO  - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
PY  - 2017
SP  - 181
EP  - 189
VL  - 51
IS  - 4
PB  - EDP-Sciences
UR  - http://www.numdam.org/articles/10.1051/ita/2017013/
DO  - 10.1051/ita/2017013
LA  - en
ID  - ITA_2017__51_4_181_0
ER  - 
%0 Journal Article
%A Currie, James D.
%A Mol, Lucas
%A Rampersad, Narad
%E Leroy, J.
%E Rigo, M.
%E Charlier, E.
%T On avoidability of formulas with reversal
%J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
%D 2017
%P 181-189
%V 51
%N 4
%I EDP-Sciences
%U http://www.numdam.org/articles/10.1051/ita/2017013/
%R 10.1051/ita/2017013
%G en
%F ITA_2017__51_4_181_0
Currie, James D.; Mol, Lucas; Rampersad, Narad. On avoidability of formulas with reversal. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Special issue dedicated to the 16th "Journées Montoises d’Informatique Théorique", Tome 51 (2017) no. 4, pp. 181-189. doi : 10.1051/ita/2017013. http://www.numdam.org/articles/10.1051/ita/2017013/

[1] D.R. Bean, A. Ehrenfeucht and G.F. Mcnulty, Avoidable patterns in strings of symbols. Pac. J. Math. 85 (1979) 261–294. | DOI | MR | Zbl

[2] J. Cassaigne, Motifs évitables et régularité dans les mots, Ph.D. Thesis. Université Paris VI (1994).

[3] R.J. Clark, Avoidable Formulas in Combinatorics on Words, Ph.D. Thesis. University of California, Los Angeles (2001). | MR

[4] J.D. Currie and P. Lafrance, Avoidability index for binary patterns with reversal. Electron. J. Combin. 23 (2016) 1–36. | DOI | MR | Zbl

[5] J.D. Currie and N. Rampersad, A proof of Dejean’s conjecture. Math. Comp. 80 (2011) 1063–1070. | DOI | MR | Zbl

[6] J.D. Currie, L. Mol and N. Rampersad, A family of formulas with reversahigl of h avoidability index. Int. J. Algebra Comput. 27 (2017) 477. | DOI | MR | Zbl

[7] M. Lothaire, Algebraic Combinatorics on Words. Cambridge University Press (2002). | DOI | Zbl

[8] M. Rao, Last cases of Dejean’s conjecture. Theoret. Comput. Sci. 412 (2011) 3010–3018. | DOI | MR | Zbl

[9] A.I. Zimin, Blocking sets of terms (English translation). Math. USSR Sbornik 47 (1984) 353–364. | DOI | MR | Zbl

Cité par Sources :