Dejean’s conjecture holds for 𝖭27
Currie, James ; Rampersad, Narad
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 43 (2009), p. 775-778 / Harvested from Numdam

We show that Dejean’s conjecture holds for n27. This brings the final resolution of the conjecture by the approach of Moulin Ollagnier within range of the computationally feasible.

Publié le : 2009-01-01
DOI : https://doi.org/10.1051/ita/2009017
Classification:  68R15
@article{ITA_2009__43_4_775_0,
     author = {Currie, James and Rampersad, Narad},
     title = {Dejean's conjecture holds for $\sf {N\ge 27}$},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     volume = {43},
     year = {2009},
     pages = {775-778},
     doi = {10.1051/ita/2009017},
     mrnumber = {2589992},
     zbl = {pre05650347},
     language = {en},
     url = {http://dml.mathdoc.fr/item/ITA_2009__43_4_775_0}
}
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) pp. 775-778. doi : 10.1051/ita/2009017. http://gdmltest.u-ga.fr/item/ITA_2009__43_4_775_0/

[1] F.J. Brandenburg, Uniformly growing k-th powerfree homomorphisms. Theoret. Comput. Sci. 23 (1983) 69-82. | MR 693069 | Zbl 0508.68051

[2] J. Brinkhuis, Non-repetitive sequences on three symbols. Quart. J. Math. Oxford 34 (1983) 145-149. | MR 698202 | Zbl 0528.05004

[3] A. Carpi, On Dejean's conjecture over large alphabets. Theoret. Comput. Sci. 385 (2007) 137-151. | MR 2356248 | Zbl 1124.68087

[4] J.D. Currie and N. Rampersad, Dejean’s conjecture holds for n30. Theoret. Comput. Sci. 410 (2009) 2885-2888. | MR 2543342 | Zbl 1173.68050

[5] J.D. Currie, N. Rampersad, A proof of Dejean's conjecture, http://arxiv.org/pdf/0905.1129v3. | Zbl 1215.68192

[6] F. Dejean, Sur un théorème de Thue. J. Combin. Theory Ser. A 13 (1972) 90-99. | MR 300959 | Zbl 0245.20052

[7] L. Ilie, P. Ochem and J. Shallit, A generalization of repetition threshold. Theoret. Comput. Sci. 345 (2005) 359-369. | MR 2171619 | Zbl 1079.68082

[8] D. Krieger, On critical exponents in fixed points of non-erasing morphisms. Theoret. Comput. Sci. 376 (2007) 70-88. | MR 2316392 | Zbl 1111.68058

[9] M. Lothaire, Combinatorics on Words, Encyclopedia of Mathematics and its Applications 17. Addison-Wesley, Reading (1983). | MR 675953 | Zbl 0514.20045

[10] F. Mignosi and G. Pirillo, Repetitions in the Fibonacci infinite word. RAIRO-Theor. Inf. Appl. 26 (1992) 199-204. | Numdam | MR 1170322 | Zbl 0761.68078

[11] M. Mohammad-Noori and J.D. Currie, Dejean's conjecture and Sturmian words. Eur. J. Combin. 28 (2007) 876-890. | MR 2300768 | Zbl 1111.68096

[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 1156042 | Zbl 0745.68085

[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 736893 | Zbl 0536.68072

[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 37.0066.17

[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 44.0462.01