Fibonacci word patterns in two-way infinite Fibonacci words

The studies of 1-Fibonacci word patterns and 0-Fibonacci word patterns were initiated by Turner (1988) [18] and Chuan (1993) [2] respectively. It is known that each proper suffix of the infinite Fibonacci word is an r-Fibonacci word pattern, r∈{0,1}. In this paper, we consider the suffixes of the tw...

Full description

Saved in:
Bibliographic Details
Published in:Theoretical computer science 2012-06, Vol.437, p.69-81
Main Authors: Chuan, Wai-Fong, Liao, Fang-Yi, Ho, Hui-Ling, Yu, Fei
Format: Article
Language:English
Subjects:
[formula omitted]-Fibonacci word pattern
Label of Fibonacci word
Mechanical word
Seed word
Sturmian morphism
Two-way infinite Fibonacci word
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:The studies of 1-Fibonacci word patterns and 0-Fibonacci word patterns were initiated by Turner (1988) [18] and Chuan (1993) [2] respectively. It is known that each proper suffix of the infinite Fibonacci word is an r-Fibonacci word pattern, r∈{0,1}. In this paper, we consider the suffixes of the two two-way infinite extensions G and G′ of the infinite Fibonacci word. We obtain necessary and sufficient conditions for suffixes of G and G′ to be r-Fibonacci word patterns. This gives us all the mechanical words with slope α=5−12 which are r-Fibonacci word patterns. All possible r-seed words of each of them are determined. Finally, images of suffixes of G and G′ under the action of certain Sturmian morphisms are computed.
ISSN:0304-3975
1879-2294
DOI:10.1016/j.tcs.2012.02.020