Ordering Words and Sets of Numbers: The Fibonacci Case

Clark Kimberling

A chapter in Applications of Fibonacci Numbers, 2004, pp 137-144 from Springer

Abstract: Abstract Let S be the set of numbers defined by these rules: 0 ∈ S and 1 ∈ S, and if x ∈ S - {0}, then 2x ∈ S and 4x + 1 ∈ S. The elements of S form a sequence s = (0, 1, 2, 4, 5, 8, 9, 10, 16, ...) that has remarkable connections with the sequence of Fibonacci numbers. For example, the positions of the even numbers in s are the positions of the 0’s in the infinite Fibonacci word, which begins with 0100010100. This ordering also matches that of the set of binary words under a certain order relation. The purpose of this paper is to explore various sequences having this ordering.

Keywords: 11B39; 11B37; 11Y83 (search for similar items in EconPapers)
Date: 2004
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DOI: 10.1007/978-0-306-48517-6_14

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