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.
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/}
}
TY - JOUR AU - Badkobeh, Golnaz AU - Crochemore, Maxime AU - Rao, Michaël TI - Finite repetition threshold for large alphabets JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications PY - 2014 SP - 419 EP - 430 VL - 48 IS - 4 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ita/2014017/ DO - 10.1051/ita/2014017 LA - en ID - ITA_2014__48_4_419_0 ER -
%0 Journal Article %A Badkobeh, Golnaz %A Crochemore, Maxime %A Rao, Michaël %T Finite repetition threshold for large alphabets %J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications %D 2014 %P 419-430 %V 48 %N 4 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ita/2014017/ %R 10.1051/ita/2014017 %G en %F ITA_2014__48_4_419_0
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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