Title

Tiling Proofs of Recent Sum Identities Involving Pell Numbers

Document Type

Article

Department

Mathematics (HMC)

Publication Date

10-2008

Abstract

In a recent note, Santana and Diaz-Barrero proved a number of sum identities involving the well-known Pell numbers. Their proofs relied heavily on the Binet formula for Pell numbers. Our goal in this note is to reconsider these identities from a purely combinatorial viewpoint. We provide bijective proofs for each of the results by interpreting the Pell numbers as enumerators of certain types of tilings. In turn, our proofs provide helpful insight for straightforward generalizations of a number of the identities.

Rights Information

© Birkhäuser Verlag, Basel, 2008

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