RAIRO-Theor. Inf. Appl.
Volume 57, 2023
|Number of page(s)||17|
|Published online||18 January 2023|
Properties of a ternary infinite word
1 Department of Math/Stats, University of Winnipeg,
515 Portage Ave.,
2 LIRMM, CNRS, Université de Montpellier, France
3 School of Computer Science, University of Waterloo, Waterloo, ON N2L 3G1, Canada
* Corresponding author: firstname.lastname@example.org
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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