|
|||||
 |
|
|
|
|
|
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/ | |
|
