Subwords of the Golden Sequence and the Fibonacci Words

Wai-fong Chuan

A chapter in Applications of Fibonacci Numbers, 1996, pp 73-84 from Springer

Abstract: 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.

Keywords: Inductive Hypothesis; Nonnegative Integer; Binary Sequence; Finite Sequence; Information Processing Letter (search for similar items in EconPapers)
Date: 1996
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-009-0223-7_7

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DOI: 10.1007/978-94-009-0223-7_7

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