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arXiv · 2511.06485

On the Asymptotic Palindrome Density of Fibonacci Infinite Words

Duaa Abdullah·Jasem Hamoud
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Abstract

In this paper, we investigate the combinatorial and density properties of infinite words generated by Fibonacci-type morphisms, focusing on their subword structure, palindrome density, and extremal statistical behaviors. Using the morphism $0 \to 01$, $1 \to 0$, we define a derived ternary word $\mathbb{Y}$ and establish new results relating its density components $\mathrm{dens}(λ,n)$, $\mathrm{dens}(α,n)$, and $\mathrm{dens}(β,n)$, deriving explicit formulae and bounds on their behavior. We further prove a general density theorem for infinite words with paired subwords, showing that the associated palindromic prefix density is bounded above by $\frac{1}{φ_1}$, where $φ_1 = (1 + \sqrt{5})/2$ is the golden ratio. Our approach connects the structure of Fibonacci and Thue--Morse sequences with precise asymptotic and combinatorial interpretations for the observed densities.

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Duaa Abdullah, Jasem Hamoud. 2026-01-18. On the Asymptotic Palindrome Density of Fibonacci Infinite Words. https://arxiv.org/abs/2511.06485

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