Currie, James; Rampersad, Narad Dejean’s conjecture holds for \(n\geq 30\). (English) Zbl 1173.68050 Theor. Comput. Sci. 410, No. 30-32, 2885-2888 (2009). Summary: We extend Carpi’s results by showing that Dejean’s conjecture holds for \(n\geq 30\). Cited in 1 ReviewCited in 16 Documents MSC: 68R15 Combinatorics on words 68Q45 Formal languages and automata Keywords:repetitive threshold; fractional power; Dejean’s conjecture PDFBibTeX XMLCite \textit{J. Currie} and \textit{N. Rampersad}, Theor. Comput. Sci. 410, No. 30--32, 2885--2888 (2009; Zbl 1173.68050) Full Text: DOI arXiv Online Encyclopedia of Integer Sequences: a(n) = n base 5, under morphism f(1) = 121, f(2) = 123, f(3) = 141, f(4) = 142, or 0 if n base 5 has a zero. References: [1] Brandenburg, F. J., Uniformly growing \(k\)-th powerfree homomorphisms, Theoret. Comput. Sci., 23, 69-82 (1983) · Zbl 0508.68051 [2] Carpi, A., On Dejean’s conjecture over large alphabets, Theoret. Comput. Sci., 385, 137-151 (2007) · Zbl 1124.68087 [3] Dejean, F., Sur un théorème de Thue, J. Combin. Theory Ser. A, 13, 90-99 (1972) · Zbl 0245.20052 [4] Ilie, L.; Ochem, P.; Shallit, J., A generalization of repetition threshold, Theoret. Comput. Sci., 345, 359-369 (2005) · Zbl 1079.68082 [5] Krieger, D., On critical exponents in fixed points of non-erasing morphisms, Theoret. Comput. Sci., 376, 70-88 (2007) · Zbl 1111.68058 [6] Mignosi, F.; Pirillo, G., Repetitions in the Fibonacci infinite word, RAIRO Inform. Théor. Appl., 26, 199-204 (1992) · Zbl 0761.68078 [7] Mohammad-Noori, M.; Currie, J. D., Dejean’s conjecture and Sturmian words, European J. Combin., 28, 876-890 (2007) · Zbl 1111.68096 [8] Moulin-Ollagnier, J., Proof of Dejean’s conjecture for alphabets with 5, 6, 7, 8, 9, 10 and 11 letters, Theoret. Comput. Sci., 95, 187-205 (1992) · Zbl 0745.68085 [9] Pansiot, J.-J., A propos d’une conjecture de F. Dejean sur les répétitions dans les mots, Discrete Appl. Math., 7, 297-311 (1984) · Zbl 0536.68072 [10] Thue, A., Über unendliche Zeichenreihen, Norske Vid. Selsk. Skr. I. Mat. Nat. Kl. Christiana, 7, 1-22 (1906) · JFM 39.0283.01 [11] Thue, A., Über die gegenseitige Lage gleicher Teile gewisser Zeichenreihen, Norske Vid. Selsk. Skr. I. Mat. Nat. Kl. Christiana, 1, 1-67 (1912) · JFM 44.0462.01 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.