Issue |
RAIRO-Theor. Inf. Appl.
Volume 54, 2020
|
|
---|---|---|
Article Number | 6 | |
Number of page(s) | 11 | |
DOI | https://doi.org/10.1051/ita/2020006 | |
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.
Winnipeg,
MB, Canada R3B 2E9.
* Corresponding author: l.mol@uwinnipeg.ca
** The work of Narad Rampersad is supported by the Natural Sciences and Engineering Research Council of Canada (NSERC), [funding reference number 2019-04111].
Received:
10
January
2020
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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