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dejean’s threshold

RAIRO - Theoretical Informatics and Applications (1)

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Finite repetition threshold for large alphabets
Golnaz Badkobeh, Maxime Crochemore, Michaël Rao
Journal:

RAIRO - Theoretical Informatics and Applications / Volume 48 / Issue 4 / October 2014

Published online by Cambridge University Press:

11 August 2014, pp. 419-430

Print publication:

October 2014
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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.