Vol. 2, No. 5, 2009

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A tiling approach to Fibonacci product identities

Jacob Artz and Michael Rowell

Vol. 2 (2009), No. 5, 581–587
Abstract

In 1998 Filipponi and Hart introduced a number of Fibonacci product identities. This paper provides a combinatorial proof for such identities via tilings. The methods used in the proof are then further used to produce some new Zeckendorf representations and a known Fibonacci identity.

Keywords
Fibonacci products, tiling
Mathematical Subject Classification 2000
Primary: 05A19, 11B39
Milestones
Received: 4 August 2009
Revised: 14 September 2009
Accepted: 19 September 2009
Published: 13 January 2010

Communicated by Arthur T. Benjamin
Authors
Jacob Artz
Mathematics Department
Pacific University
2043 College Way
Forest Grove, OR 97116
United States
Michael Rowell
Mathematics Department
Pacific University
2043 College Way
Forest Grove, OR 97116
United States
www.math.pacificu.edu/~rowell