
Jiemeng Zhang

Zhixiong Wen

Wen Wu
Keywords:
Infinite Fibonacci sequence, Singular words, Fibonacci number, Digit sum
Abstract
The infinite Fibonacci sequence $\mathbf{F}$, which is an extension of the classic Fibonacci sequence to the infinite alphabet $\mathbb{N}$, is the fixed point of the morphism $\phi$: $(2i)\mapsto (2i)(2i+1)$ and $(2i+1)\mapsto (2i+2)$ for all $i\in\mathbb{N}$. In this paper, we study the growth order and digit sum of $\mathbf{F}$ and give several decompositions of $\mathbf{F}$ using singular words.
Author Biographies
Jiemeng Zhang, Wuhan Institute of Technology
PhD in Math.
Lecuturer, Wuhan institute of Technology
Zhixiong Wen, Huazhong University of Science and Technology
Professor in Mathematics,
Huazhong University of Science and Technology
Wen Wu, South China University of Technology
PhD in Math.
Lecturer, School of Mathematics, South China University of Technology