Around the Fibonacci Numeration System

Description:

Let 1, 2, 3, 5, 8, … denote the Fibonacci sequence beginning with 1 and 2, and then setting each subsequent number to the sum of the two previous ones. Every positive integer n can be expressed as a sum of distinct Fibonacci numbers in one or more ways. Setting R(n) to be the number of ways n can be written as a sum of distinct Fibonacci numbers, we exhibit certain regularity properties of R(n), one of which is connected to the Euler φ-function. In addition, using a theorem of Fine and Wilf, we give a formula for R(n) in terms of binomial coefficients modulo two.

Creator(s): Edson, Marcia Ruth
Creation Date: May 2007
Partner(s):
UNT Libraries
Collection(s):
UNT Theses and Dissertations
Usage:
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Past 30 days: 3
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Publisher Info:
Publisher Name: University of North Texas
Place of Publication: Denton, Texas
Date(s):
  • Creation: May 2007
  • Digitized: August 3, 2007
Description:

Let 1, 2, 3, 5, 8, … denote the Fibonacci sequence beginning with 1 and 2, and then setting each subsequent number to the sum of the two previous ones. Every positive integer n can be expressed as a sum of distinct Fibonacci numbers in one or more ways. Setting R(n) to be the number of ways n can be written as a sum of distinct Fibonacci numbers, we exhibit certain regularity properties of R(n), one of which is connected to the Euler φ-function. In addition, using a theorem of Fine and Wilf, we give a formula for R(n) in terms of binomial coefficients modulo two.

Degree:
Level: Doctoral
Discipline: Mathematics
Language(s):
Subject(s):
Keyword(s): Numeration systems | Fine and Wilf theorem | general and Euclidian algorithms
Contributor(s):
Partner:
UNT Libraries
Collection:
UNT Theses and Dissertations
Identifier:
  • OCLC: 179921850 |
  • ARK: ark:/67531/metadc3676
Resource Type: Thesis or Dissertation
Format: Text
Rights:
Access: Public
License: Copyright
Holder: Edson, Marcia Ruth
Statement: Copyright is held by the author, unless otherwise noted. All rights reserved.