Tiling proofs of recent sum identities involving Pell numbers

Arthur T. Benjamin, Sean S. Plott, James A. Sellers

Research output: Contribution to journalArticle

15 Scopus citations

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 the 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.

Original languageEnglish (US)
Pages (from-to)271-278
Number of pages8
JournalAnnals of Combinatorics
Volume12
Issue number3
DOIs
StatePublished - Oct 2008

All Science Journal Classification (ASJC) codes

  • Discrete Mathematics and Combinatorics

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