Some properties of the singular words of the Fibonacci word
European Journal of Combinatorics
The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
&agr;-words and factors of characteristic sequences
Discrete Mathematics
A representation theorem of the suffixes of characteristic sequences
Discrete Applied Mathematics
Unbordered factors of the characteristic sequences of irrational numbers
Theoretical Computer Science
Factors of characteristic words of irrational numbers
Theoretical Computer Science
Factors of characteristic words: Location and decompositions
Theoretical Computer Science
A simple representation of subwords of the Fibonacci word
Information Processing Letters
Theoretical Computer Science
Fibonacci word patterns in two-way infinite Fibonacci words
Theoretical Computer Science
Locating factors of a characteristic word via the generalized Zeckendorf representation of numbers
Theoretical Computer Science
Discrete Applied Mathematics
| Hi-index | 5.23 |
Let τ = (√5 - 1)/2. Let a, b be two distinct letters. The infinite Fibonacci word is the infinite word G = babbababbabbababbababbabba... whose nth letter is a (resp., b) if [(n + 1)τ] - [nτ] = 0 (resp., 1). For a factor w of G, the location of w is the set of all positions in G at which w occurs. Only the locations of the following factors of G are already known: squares, singular words and those factors of G whose lengths are Fibonacci numbers. The purpose of this paper is to determine the locations of all factors of G. Our results contain all the known ones as consequences. Moreover, using our results, we are able to identify any factor of G whenever its starting position and length are given; also we are able to tell whether two suffixes of G have a common prefix of a certain length.