| Issue |
RAIRO-Theor. Inf. Appl.
Volume 57, 2023
|
|
|---|---|---|
| Article Number | 1 | |
| Number of page(s) | 17 | |
| DOI | https://doi.org/10.1051/ita/2022010 | |
| Published online | 18 January 2023 | |
Properties of a ternary infinite word
1 Department of Math/Stats, University of Winnipeg,
515 Portage Ave.,
Winnipeg
R3B 2E9,
MB,
Canada
2 LIRMM, CNRS, Université de Montpellier,
France
3 School of Computer Science, University of Waterloo,
Waterloo,
ON
N2L 3G1,
Canada
* Corresponding author: shallit@uwaterloo.ca
Received:
19
September
2022
Accepted:
5
December
2022
We study the properties of the ternary infinite word
p = 012102101021012101021012⋯,
that is, the fixed point of the map h : 0 → 01, 1 → 21, 2 → 0. We determine its factor complexity, critical exponent, and prove that it is 2-balanced. We compute its abelian complexity and determine the lengths of its bispecial factors. Finally, we give a characterization of p in terms of avoided factors.
Mathematics Subject Classification: 11B85 / 68R15 / 03D05 / 68Q45
Key words: Factor complexity / critical exponent / Pisot numeration system / automatic sequence / linear representation / finite automaton / synchronized sequence / balanced word / abelian complexity / recurrence / appearance
© The authors. Published by EDP Sciences, 2023
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