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.
@article{10_37236_6745,
author = {Jiemeng Zhang and Zhixiong Wen and Wen Wu},
title = {Some properties of the {Fibonacci} sequence on an infinite alphabet},
journal = {The electronic journal of combinatorics},
year = {2017},
volume = {24},
number = {2},
doi = {10.37236/6745},
zbl = {1366.11038},
url = {http://geodesic.mathdoc.fr/articles/10.37236/6745/}
}
TY - JOUR
AU - Jiemeng Zhang
AU - Zhixiong Wen
AU - Wen Wu
TI - Some properties of the Fibonacci sequence on an infinite alphabet
JO - The electronic journal of combinatorics
PY - 2017
VL - 24
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.37236/6745/
DO - 10.37236/6745
ID - 10_37236_6745
ER -
%0 Journal Article
%A Jiemeng Zhang
%A Zhixiong Wen
%A Wen Wu
%T Some properties of the Fibonacci sequence on an infinite alphabet
%J The electronic journal of combinatorics
%D 2017
%V 24
%N 2
%U http://geodesic.mathdoc.fr/articles/10.37236/6745/
%R 10.37236/6745
%F 10_37236_6745
Jiemeng Zhang; Zhixiong Wen; Wen Wu. Some properties of the Fibonacci sequence on an infinite alphabet. The electronic journal of combinatorics, Tome 24 (2017) no. 2. doi: 10.37236/6745
