Finite repetition threshold for large alphabets
Received: 14 March 2014
Accepted: 17 March 2014
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.
Mathematics Subject Classification: 68R15
Key words: Morphisms / repetitions in words / Dejean’s threshold
© EDP Sciences 2014