Decision Algorithms for Fibonacci-Automatic Words, with Applications to Pattern Avoidance

@article{Du2014DecisionAF,
  title={Decision Algorithms for Fibonacci-Automatic Words, with Applications to Pattern Avoidance},
  author={Chen Fei Du and Hamoon Mousavi and Luke Schaeffer and Jeffrey Shallit},
  journal={CoRR},
  year={2014},
  volume={abs/1406.0670}
}
We implement a decision procedure for answering questions about a class of infinite words that might be called (for lack of a better name) “Fibonacci-automatic”. This class includes, for example, the famous Fibonacci word f = 01001010 · · · , the fixed point of the morphism 0→ 01 and 1→ 0. We then recover many results about the Fibonacci word from the literature (and improve some of them), such as assertions about the occurrences in f of squares, cubes, palindromes, and so forth. As an… CONTINUE READING
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References

Publications referenced by this paper.
Showing 1-10 of 74 references

Weak Repetitions in Strings

View 4 Excerpts
Highly Influenced

Borders of Fibonacci strings

L. J. Cummings, D. Moore, J. Karhumäki
J. Combin. Math. Combin. Comput. 20 • 1996
View 4 Excerpts
Highly Influenced

Symmetric Fibonacci words

W.-F. Chuan
Fibonacci Quart. 31 • 1993
View 6 Excerpts
Highly Influenced

Propriétés combinatoires des mots infinis engendrés par certains morphismes (Thèse de 3 cycle)

P. Séébold
PhD thesis, Université P. et M. Curie, Institut de Programmation, Paris • 1985
View 4 Excerpts
Highly Influenced

Lyndon words and Fibonacci numbers

J. Comb. Theory, Ser. A • 2014
View 5 Excerpts
Highly Influenced

Least Periods of Factors of Infinite Words

View 5 Excerpts
Highly Influenced

On Maximal Repetitions in Words

View 3 Excerpts
Highly Influenced

The Exact Number of Squares in Fibonacci Words

Theor. Comput. Sci. • 1999
View 5 Excerpts
Highly Influenced

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