More properties of the Fibonacci word on an infinite alphabet

TL;DR

This paper explores the Fibonacci word on an infinite alphabet, analyzing its structural properties such as squares, palindromes, and Lyndon factors, revealing new combinatorial insights about this infinite word.

Contribution

It provides new results on the occurrence and structure of squares, palindromes, and Lyndon factors within the Fibonacci word on an infinite alphabet.

Findings

Characterization of squares in the Fibonacci word

Identification of palindromes and their distribution

Analysis of Lyndon factors in the infinite Fibonacci word

Abstract

Recently the Fibonacci word $W$ on an infinite alphabet was introduced by [Zhang et al., Electronic J. Combinatorics 24-2 (2017) #P2.52] as a fixed point of the morphism $\phi: (2i) \mapsto (2i)(2i+ 1),\ (2i+ 1) \mapsto (2i+ 2)$ over all $i \in \mathbb{N}$. In this paper we investigate the occurrence of squares, palindromes, and Lyndon factors in this infinite word.