Counting Fibonacci Identities

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 work continues the work done by Artz and Rowell to many of the remaining identities from Filiponni and Hart's work. We then close by answering an open problem raised by Artz and Rowell and present many Zeckendorf representations of mixed products that involve three variables.