Properties of a Ternary Infinite Word

Abstract

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.