Properties of a ternary infinite word

James Currie,Pascal Ochem,Narad Rampersad,Jeffrey Shallit

arxiv（2023）

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摘要

We study the properties of the ternary infinite wordp = 012102101021012101021012MIDLINE HORIZONTAL ELLIPSIS,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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关键词

Factor complexity,critical exponent,Pisot numeration system,automatic sequence,linear representation,finite automaton,synchronized sequence,balanced word,abelian complexity,recurrence,appearance

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