We show that Dejean’s conjecture holds for . This brings the final resolution of the conjecture by the approach of Moulin Ollagnier within range of the computationally feasible.
@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] Uniformly growing -th powerfree homomorphisms. Theoret. Comput. Sci. 23 (1983) 69-82. | MR 693069 | Zbl 0508.68051
,[2] Non-repetitive sequences on three symbols. Quart. J. Math. Oxford 34 (1983) 145-149. | MR 698202 | Zbl 0528.05004
,[3] On Dejean's conjecture over large alphabets. Theoret. Comput. Sci. 385 (2007) 137-151. | MR 2356248 | Zbl 1124.68087
,[4] Dejean’s conjecture holds for . Theoret. Comput. Sci. 410 (2009) 2885-2888. | MR 2543342 | Zbl 1173.68050
and ,[5] A proof of Dejean's conjecture, http://arxiv.org/pdf/0905.1129v3. | Zbl 1215.68192
, ,[6] Sur un théorème de Thue. J. Combin. Theory Ser. A 13 (1972) 90-99. | MR 300959 | Zbl 0245.20052
,[7] A generalization of repetition threshold. Theoret. Comput. Sci. 345 (2005) 359-369. | MR 2171619 | Zbl 1079.68082
, and ,[8] On critical exponents in fixed points of non-erasing morphisms. Theoret. Comput. Sci. 376 (2007) 70-88. | MR 2316392 | Zbl 1111.68058
,[9] Combinatorics on Words, Encyclopedia of Mathematics and its Applications 17. Addison-Wesley, Reading (1983). | MR 675953 | Zbl 0514.20045
,[10] Repetitions in the Fibonacci infinite word. RAIRO-Theor. Inf. Appl. 26 (1992) 199-204. | Numdam | MR 1170322 | Zbl 0761.68078
and ,[11] Dejean's conjecture and Sturmian words. Eur. J. Combin. 28 (2007) 876-890. | MR 2300768 | Zbl 1111.68096
and ,[12] 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] 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] Last cases of Dejean's Conjecture, http://www.labri.fr/perso/rao/publi/dejean.ps.
,[15] Über unendliche Zeichenreihen. Norske Vid. Selsk. Skr. I. Mat. Nat. Kl. Christiana 7 (1906) 1-22. | JFM 37.0066.17
,[16] 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
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