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Dejean’s conjecture holds for \({n\geq 27}\). (English) Zbl 1192.68497

Summary: We show that Dejean’s conjecture holds for \(n\geq 27\). This brings the final resolution of the conjecture by the approach of Moulin Ollagnier within range of the computationally feasible.

MSC:

68R15 Combinatorics on words
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References:

[1] F.J. Brandenburg, Uniformly growing k-th powerfree homomorphisms. Theoret. Comput. Sci.23 (1983) 69-82. · Zbl 0508.68051
[2] J. Brinkhuis, Non-repetitive sequences on three symbols. Quart. J. Math. Oxford34 (1983) 145-149. Zbl0528.05004 · Zbl 0528.05004
[3] A. Carpi, On Dejean’s conjecture over large alphabets. Theoret. Comput. Sci.385 (2007) 137-151. Zbl1124.68087 · Zbl 1124.68087
[4] J.D. Currie and N. Rampersad, Dejean’s conjecture holds for n \geq 30. Theoret. Comput. Sci.410 (2009) 2885-2888. · Zbl 1173.68050
[5] J.D. Currie, N. Rampersad, A proof of Dejean’s conjecture, . URIhttp://arxiv.org/pdf/0905.1129v3 · Zbl 1215.68192
[6] F. Dejean, Sur un théorème de Thue. J. Combin. Theory Ser. A13 (1972) 90-99. · Zbl 0245.20052
[7] L. Ilie, P. Ochem and J. Shallit, A generalization of repetition threshold. Theoret. Comput. Sci.345 (2005) 359-369. · Zbl 1079.68082
[8] D. Krieger, On critical exponents in fixed points of non-erasing morphisms. Theoret.Comput. Sci.376 (2007) 70-88. · Zbl 1111.68058
[9] M. Lothaire, Combinatorics on Words, Encyclopedia of Mathematics and its Applications 17. Addison-Wesley, Reading (1983). · Zbl 0514.20045
[10] F. Mignosi and G. Pirillo, Repetitions in the Fibonacci infinite word. RAIRO-Theor. Inf. Appl.26 (1992) 199-204. · Zbl 0761.68078
[11] M. Mohammad-Noori and J.D. Currie, Dejean’s conjecture and Sturmian words. Eur. J. Combin.28 (2007) 876-890. Zbl1111.68096 · 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. Zbl0745.68085 · 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. Zbl0536.68072 · Zbl 0536.68072
[14] M. Rao, Last cases of Dejean’s Conjecture, . URIhttp://www.labri.fr/perso/rao/publi/dejean.ps · Zbl 1230.68163
[15] A. Thue, Über unendliche Zeichenreihen. Norske Vid. Selsk. Skr. I. Mat. Nat. Kl. Christiana7 (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. Christiana1 (1912) 1-67. · JFM 44.0462.01
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