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Subwords of the Golden Sequence and the Fibonacci Words

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Applications of Fibonacci Numbers

Abstract

A word w is called an nth order Fibonacci word derived from a pair (a,b) of distinct letters if there exists a finite sequence w1,w2,…,w n of words with w1 = a, w2 = b, wn = w and each wk equals wk−1wk−2 or wk−2wk−1, 3 ≤ k ≤ n. The basic structure and properties of Fibonacci words have been studied in [2–6]. In this paper, we determine all the prefixes of Fibonacci words and the subwords of the golden sequence that are of Fibonacci lengths.

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References

  1. Anderson, P.G. Private communication, 1992.

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  2. Chuan, W. “Fibonacci Words”. The Fibonacci Quarterly, Vol. 30.1 (1992): pp. 68–76.

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  3. Chuan, W. “Symmetric Fibonacci Words”. The Fibonacci Quarterly, Vol. 31.3 (1993): pp. 251–255.

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  5. Chuan, W. “Generating Fibonacci Words”. The Fibonacci Quarterly, to appear.

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  6. De Luca, A. “A Combinatorial Property of the Fibonacci Words”. Information Processing Letter 12 (1981): pp. 193–195.

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Authors
  1. Wai-fong Chuan
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Editor information

Editors and Affiliations

  1. Computer Science Department, South Dakota State University, Box 2201, 57007-1596, Brookings, South Dakota, USA

    Gerald E. Bergum

  2. 26 Atlantis Street, Aglangia, Nicosia, Cyprus

    Andreas N. Philippou

  3. Department of Mathematics, Statistics and Computer Science, The University of New England, Armidale, New South Wales, 2351, Australia

    Alwyn F. Horadam

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© 1996 Kluwer Academic Publishers

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Chuan, Wf. (1996). Subwords of the Golden Sequence and the Fibonacci Words. In: Bergum, G.E., Philippou, A.N., Horadam, A.F. (eds) Applications of Fibonacci Numbers. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-0223-7_7

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  • DOI: https://doi.org/10.1007/978-94-009-0223-7_7

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-6583-2

  • Online ISBN: 978-94-009-0223-7

  • eBook Packages: Springer Book Archive

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