More properties of the Fibonacci word on an infinite alphabet

Recently the Fibonacci word W on an infinite alphabet was introduced by Zhang et al. (2017) [13] as a fixed point of the morphism ϕ : ( 2 i ) ↦ ( 2 i ) ( 2 i + 1 ) , ( 2 i + 1 ) ↦ ( 2 i + 2 ) over all i ∈ N . In this paper we investigate the occurrence of squares, palindromes, and Lyndon factors in this infinite word.