Properties of a Ternary Infinite Word

2022/06/03 by James D. Currie, Currie, James, Pascal Ochem +5 · 3 citations
Computer Science · #Advanced Algebra and Logic #Coding theory and cryptography #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #Dynamical Systems (math.DS) #FOS: Computer and information sciences #FOS: Mathematics #Formal Languages and Automata Theory (cs.FL) #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.2206.01776

openalex publication_date 2022/06/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• Words with factor complexity 2n+1 and minimal critical exponent
• Critical exponent of ternary words with few distinct palindromes
• Low complexity binary words avoiding (5/2)⁺-powers

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