Properties of a Ternary Infinite Word

TL;DR

This paper analyzes the combinatorial properties of a specific ternary infinite word, including its complexity, balance, and factor structure, providing a comprehensive characterization of its structure and behavior.

Contribution

It introduces a detailed analysis of the ternary infinite word p, including new results on its factor complexity, abelian complexity, and characterization in terms of avoided factors.

Findings

Determined the factor complexity of p.

Proved p is 2-balanced.

Computed the abelian complexity and bispecial factors of p.

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.