Vol. 4, No. 1, 2011

Download this article
Download this article For screen
For printing
Recent Issues

Volume 10
Issue 5, 721–900
Issue 4, 541–720
Issue 3, 361–539
Issue 2, 181–360
Issue 1, 1–180

Volume 9, 5 issues

Volume 8, 5 issues

Volume 7, 6 issues

Volume 6, 4 issues

Volume 5, 4 issues

Volume 4, 4 issues

Volume 3, 4 issues

Volume 2, 5 issues

Volume 1, 2 issues

The Journal
Cover Page
Editorial Board
Editors’ Addresses
Editors’ Interests
About the Journal
Scientific Advantages
Submission Guidelines
Submission Form
Ethics Statement
Subscriptions
Editorial Login
Author Index
Coming Soon
Contacts
 
ISSN: 1944-4184 (e-only)
ISSN: 1944-4176 (print)
Combinatorial proofs of Zeckendorf representations of Fibonacci and Lucas products

Duncan McGregor and Michael Jason Rowell

Vol. 4 (2011), No. 1, 75–89
Abstract

In 1998, Filipponi and Hart introduced many Zeckendorf representations of Fibonacci, Lucas and mixed products involving two variables. In 2008, Artz and Rowell proved the simplest of these identities, the Fibonacci product, using tilings. This paper extends the work done by Artz and Rowell to many of the remaining identities from Filipponi and Hart’s work. We also answer an open problem raised by Artz and Rowell and present many Zeckendorf representations of mixed products involving three variables.

Keywords
number theory, Fibonacci numbers, Zeckendorf representations, combinatorics
Mathematical Subject Classification 2000
Primary: 05A19, 11B39
Milestones
Received: 10 August 2010
Accepted: 24 October 2010
Published: 22 September 2011

Proposed: Arthur T. Benjamin
Communicated by Arthur T. Benjamin
Authors
Duncan McGregor
Department of Mathematics and Computer Science
Pacific University
2043 College Way
Forest Grove, OR 97116
United States
Michael Jason Rowell
Department of Mathematics and Computer Science
Pacific University
2043 College Way
Forest Grove, OR 97116
United States
http://www.pacificu.edu/as/math/