Finite repetition threshold for large alphabets
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 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 : https://doi.org/10.1051/ita/2014017
Classification : 68R15
Mots clés : morphisms, repetitions in words, Dejean's threshold
@article{ITA_2014__48_4_419_0,
     author = {Badkobeh, Golnaz and Crochemore, Maxime and Rao, Micha\"el},
     title = {Finite repetition threshold for large alphabets},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {419--430},
     publisher = {EDP-Sciences},
     volume = {48},
     number = {4},
     year = {2014},
     doi = {10.1051/ita/2014017},
     mrnumber = {3302495},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/ita/2014017/}
}
Badkobeh, Golnaz; Crochemore, Maxime; Rao, Michaël. Finite repetition threshold for large alphabets. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 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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