no. 4
Dejean’s conjecture holds for 𝖭≥27
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 43 (2009) no. 4, pp. 775-778.

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

DOI : 10.1051/ita/2009017
Classification : 68R15
Mots clés : Dejean's conjecture, repetitions in words, fractional exponent 
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     author = {Currie, James and Rampersad, Narad},
     title = {Dejean{\textquoteright}s conjecture holds for $\sf {N\ge 27}$},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {775--778},
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Currie, James; Rampersad, Narad. Dejean’s conjecture holds for $\sf {N\ge 27}$. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 43 (2009) no. 4, pp. 775-778. doi : 10.1051/ita/2009017. http://archive.numdam.org/articles/10.1051/ita/2009017/

[1] F.J. Brandenburg, Uniformly growing k-th powerfree homomorphisms. Theoret. Comput. Sci. 23 (1983) 69-82. | MR | Zbl

[2] J. Brinkhuis, Non-repetitive sequences on three symbols. Quart. J. Math. Oxford 34 (1983) 145-149. | MR | Zbl

[3] A. Carpi, On Dejean's conjecture over large alphabets. Theoret. Comput. Sci. 385 (2007) 137-151. | MR | Zbl

[4] J.D. Currie and N. Rampersad, Dejean’s conjecture holds for n≥30. Theoret. Comput. Sci. 410 (2009) 2885-2888. | MR | Zbl

[5] J.D. Currie, N. Rampersad, A proof of Dejean's conjecture, http://arxiv.org/pdf/0905.1129v3. | Zbl

[6] F. Dejean, Sur un théorème de Thue. J. Combin. Theory Ser. A 13 (1972) 90-99. | MR | Zbl

[7] L. Ilie, P. Ochem and J. Shallit, A generalization of repetition threshold. Theoret. Comput. Sci. 345 (2005) 359-369. | MR | Zbl

[8] D. Krieger, On critical exponents in fixed points of non-erasing morphisms. Theoret. Comput. Sci. 376 (2007) 70-88. | MR | Zbl

[9] M. Lothaire, Combinatorics on Words, Encyclopedia of Mathematics and its Applications 17. Addison-Wesley, Reading (1983). | MR | Zbl

[10] F. Mignosi and G. Pirillo, Repetitions in the Fibonacci infinite word. RAIRO-Theor. Inf. Appl. 26 (1992) 199-204. | Numdam | MR | Zbl

[11] M. Mohammad-Noori and J.D. Currie, Dejean's conjecture and Sturmian words. Eur. J. Combin. 28 (2007) 876-890. | MR | Zbl

[12] J. Moulin Ollagnier, Proof of Dejean's conjecture for alphabets with 5, 6, 7, 8, 9, 10 and 11 letters. Theoret. Comput. Sci. 95 (1992) 187-205. | MR | Zbl

[13] J.-J. Pansiot, À propos d'une conjecture de F. Dejean sur les répétitions dans les mots. Discrete Appl. Math. 7 (1984) 297-311. | MR | Zbl

[14] M. Rao, Last cases of Dejean's Conjecture, http://www.labri.fr/perso/rao/publi/dejean.ps.

[15] A. Thue, Über unendliche Zeichenreihen. Norske Vid. Selsk. Skr. I. Mat. Nat. Kl. Christiana 7 (1906) 1-22. | JFM

[16] A. Thue, Über die gegenseitige Lage gleicher Teile gewisser Zeichenreihen. Norske Vid. Selsk. Skr. I. Mat. Nat. Kl. Christiana 1 (1912) 1-67. | JFM

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