Involve: A Journal of Mathematics
- Volume 4, Number 1 (2011), 75-89.
Combinatorial proofs of Zeckendorf representations of Fibonacci and Lucas products
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.
Involve, Volume 4, Number 1 (2011), 75-89.
Received: 10 August 2010
Accepted: 24 October 2010
First available in Project Euclid: 20 December 2017
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McGregor, Duncan; Rowell, Michael. Combinatorial proofs of Zeckendorf representations of Fibonacci and Lucas products. Involve 4 (2011), no. 1, 75--89. doi:10.2140/involve.2011.4.75. https://projecteuclid.org/euclid.involve/1513733364