IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-0-306-48517-6_14.html
   My bibliography  Save this book chapter

Ordering Words and Sets of Numbers: The Fibonacci Case

In: Applications of Fibonacci Numbers

Author

Listed:
  • Clark Kimberling

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.

Suggested Citation

  • Clark Kimberling, 2004. "Ordering Words and Sets of Numbers: The Fibonacci Case," Springer Books, in: Frederic T. Howard (ed.), Applications of Fibonacci Numbers, pages 137-144, Springer.
    • Handle: RePEc:spr:sprchp:978-0-306-48517-6_14
    DOI: 10.1007/978-0-306-48517-6_14
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    More about this item

    Keywords

    ;
    ;
    ;

    JEL classification:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:sprchp:978-0-306-48517-6_14. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.