The repetition threshold for words on n letters, denoted RT(n), is the infimum of the set of all r such that there are arbitrarily long r-free words over n letters. A repetition threshold for circular words on n letters can be defined in three natural ways, which gives rise to the weak, intermediate, and strong circular repetition thresholds for n letters, denoted CRTW(n), CRTI(n), and CRTS(n), respectively. Currie and the present authors conjectured that CRTI(n) = CRTW(n) = RT(n) for all n ≥ 4. We prove that CRTW(n) = RT(n) for all n ≥ 45, which confirms a weak version of this conjecture for all but finitely many values of n.
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DOI : 10.1051/ita/2020006
Mots-clés : Repetition threshold, circular repetition threshold, repetition threshold for graphs, Dejean’s conjecture, Dejean’s theorem, nonrepetitive colouring
@article{ITA_2020__54_1_A6_0,
author = {Mol, Lucas and Rampersad, Narad},
title = {The weak circular repetition threshold over large alphabets},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
publisher = {EDP-Sciences},
volume = {54},
year = {2020},
doi = {10.1051/ita/2020006},
mrnumber = {4169251},
zbl = {1508.68272},
language = {en},
url = {http://www.numdam.org/articles/10.1051/ita/2020006/}
}
TY - JOUR AU - Mol, Lucas AU - Rampersad, Narad TI - The weak circular repetition threshold over large alphabets JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications PY - 2020 VL - 54 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ita/2020006/ DO - 10.1051/ita/2020006 LA - en ID - ITA_2020__54_1_A6_0 ER -
%0 Journal Article %A Mol, Lucas %A Rampersad, Narad %T The weak circular repetition threshold over large alphabets %J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications %D 2020 %V 54 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ita/2020006/ %R 10.1051/ita/2020006 %G en %F ITA_2020__54_1_A6_0
Mol, Lucas; Rampersad, Narad. The weak circular repetition threshold over large alphabets. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 54 (2020), article no. 6. doi : 10.1051/ita/2020006. http://www.numdam.org/articles/10.1051/ita/2020006/
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