Involve: A Journal of Mathematics

  • Involve
  • Volume 4, Number 1 (2011), 75-89.

Combinatorial proofs of Zeckendorf representations of Fibonacci and Lucas products

Duncan McGregor and Michael Rowell

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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.

Article information

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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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 05A19: Combinatorial identities, bijective combinatorics 11B39: Fibonacci and Lucas numbers and polynomials and generalizations

number theory Fibonacci numbers Zeckendorf representations combinatorics


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.

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