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Properties of a ternary infinite word
Article de revue   Open Access   Avec comité de lecture

Properties of a ternary infinite word

James Currie, Pascal Ochem, Narad Rampersad et Jeffrey Shallit
RAIRO - Theoretical Informatics and Applications (RAIRO: ITA), Vol.57
2023

Résumé

Factor complexity Critical exponent Pisot numeration system Automatic sequence Linear representation Finite automaton Synchronized sequence Balanced word Abelian complexity Recurrence Appearance
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.

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