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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 pointof the morphism $\phi: (2i) \mapsto (2i)(2i+ 1),\ (2i+ 1) \mapsto (2i+ 2)$ overall $i \in \mathbb{N}$. In this paper we investigate the occurrence of squares,palindromes, and Lyndon factors in this infinite word.

More properties of the Fibonacci word on an infinite alphabet