RAIRO-Theor. Inf. Appl.
Volume 54, 2020
|Number of page(s)||11|
|Published online||02 November 2020|
The weak circular repetition threshold over large alphabets
Department of Mathematics and Statistics, The University of Winnipeg,
515 Portage Ave.
MB, Canada R3B 2E9.
* Corresponding author: firstname.lastname@example.org
** The work of Narad Rampersad is supported by the Natural Sciences and Engineering Research Council of Canada (NSERC), [funding reference number 2019-04111].
Accepted: 21 September 2020
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.
Mathematics Subject Classification: 68R15 / 05C15
Key words: Repetition threshold / circular repetition threshold / repetition threshold for graphs / Dejean’s conjecture / Dejean’s theorem / nonrepetitive colouring
© EDP Sciences, 2020
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