| Issue |
RAIRO-Theor. Inf. Appl.
Volume 58, 2024
|
|
|---|---|---|
| Article Number | 14 | |
| Number of page(s) | 11 | |
| DOI | https://doi.org/10.1051/ita/2024011 | |
| Published online | 22 April 2024 | |
A Small Morphism for which the Fixed Point has an Abelian Critical Exponent Less than 2
Department of Mathematics & Statistics, The University of Winnipeg, Winnipeg, Canada
* Corresponding author: j.currie@uwinnipeg.ca
Received:
30
December
2023
Accepted:
29
March
2024
It is known that there are infinite words over finite alphabets with Abelian critical exponent arbitrarily close to 1; however, the construction previously used involves huge alphabets. In this note we give a short cyclic morphism (length 13) over an 8-letter alphabet for which the fixed point has an Abelian critical exponent less than 1.8.
Mathematics Subject Classification: 68R15
Key words: Abelian repetition / Dejean’s conjecture / critical exponent / repetition threshold / combinatorics on words
© The authors. Published by EDP Sciences, 2024
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