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Dejean's conjecture holds for N ≥ 27

Published online by Cambridge University Press:  29 September 2009

James Currie  and
Narad Rampersad
James Currie
Affiliation:
Department of Mathematics and Statistics, University of Winnipeg, 515 Portage Avenue, Winnipeg, Manitoba R3B 2E9, Canada; [email protected]
Narad Rampersad
Affiliation:
Department of Mathematics and Statistics, University of Winnipeg, 515 Portage Avenue, Winnipeg, Manitoba R3B 2E9, Canada; [email protected]
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Abstract

We show that Dejean's conjectureholds for n ≥ 27. This brings the final resolution of the conjecture by the approach of Moulin Ollagnier within range of the computationally feasible.

Keywords

Dejean's conjecturerepetitions in wordsfractional exponent.
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 43 , Issue 4 , October 2009 , pp. 775 - 778
Copyright
© EDP Sciences, 2009

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References

Brandenburg, F.J., Uniformly growing k-th powerfree homomorphisms. Theoret. Comput. Sci. 23 (1983) 69–82. CrossRef
Brinkhuis, J., Non-repetitive sequences on three symbols. Quart. J. Math. Oxford 34 (1983) 145–149. CrossRef
Carpi, A., Dejean's, On conjecture over large alphabets. Theoret. Comput. Sci. 385 (2007) 137–151. CrossRef
Currie, J.D. and Rampersad, N., Dejean's conjecture holds for n ≥ 30. Theoret. Comput. Sci. 410 (2009) 2885–2888. CrossRef
J.D. Currie, N. Rampersad, A proof of Dejean's conjecture, http://arxiv.org/pdf/0905.1129v3.
Dejean, F., Sur un théorème de Thue. J. Combin. Theory Ser. A 13 (1972) 90–99. CrossRef
Ilie, L., Ochem, P. and Shallit, J., A generalization of repetition threshold. Theoret. Comput. Sci. 345 (2005) 359–369. CrossRef
D. Krieger, On critical exponents in fixed points of non-erasing morphisms. Theoret. Comput. Sci. 376 (2007) 70–88.
M. Lothaire, Combinatorics on Words, Encyclopedia of Mathematics and its Applications 17. Addison-Wesley, Reading (1983).
Mignosi, F. and Pirillo, G., Repetitions in the Fibonacci infinite word. RAIRO-Theor. Inf. Appl. 26 (1992) 199–204. CrossRef
Mohammad-Noori, M. and Currie, J.D., Dejean's conjecture and Sturmian words. Eur. J. Combin. 28 (2007) 876–890. CrossRef
Moulin Ollagnier, J., Proof of Dejean's conjecture for alphabets with 5, 6, 7, 8, 9, 10 and 11 letters. Theoret. Comput. Sci. 95 (1992) 187–205. CrossRef
Pansiot, J.-J., À propos d'une conjecture de F. Dejean sur les répétitions dans les mots. Discrete Appl. Math. 7 (1984) 297–311. CrossRef
M. Rao, Last cases of Dejean's Conjecture, http://www.labri.fr/perso/rao/publi/dejean.ps.
Thue, A., Über unendliche Zeichenreihen. Norske Vid. Selsk. Skr. I. Mat. Nat. Kl. Christiana 7 (1906) 1–22.
Thue, A., Über die gegenseitige Lage gleicher Teile gewisser Zeichenreihen. Norske Vid. Selsk. Skr. I. Mat. Nat. Kl. Christiana 1 (1912) 1–67.