Finite repetition threshold for large alphabets
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Volume 48 (2014) no. 4, pp. 419-430.

We investigate the finite repetition threshold for k-letter alphabets, k ≥ 4, that is the smallest number r for which there exists an infinite r+-free word containing a finite number of r-powers. We show that there exists an infinite Dejean word on a 4-letter alphabet (i.e. a word without factors of exponent more than 7/5 ) containing only two 7/5 -powers. For a 5-letter alphabet, we show that there exists an infinite Dejean word containing only 60 5/4 -powers, and we conjecture that this number can be lowered to 45. Finally we show that the finite repetition threshold for k letters is equal to the repetition threshold for k letters, for every k ≥ 6.

DOI: 10.1051/ita/2014017
Classification: 68R15
Keywords: morphisms, repetitions in words, Dejean's threshold
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Badkobeh, Golnaz; Crochemore, Maxime; Rao, Michaël. Finite repetition threshold for large alphabets. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Volume 48 (2014) no. 4, pp. 419-430. doi : 10.1051/ita/2014017. http://www.numdam.org/articles/10.1051/ita/2014017/

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