Tiling Proofs of Recent Sum Identities Involving Pell Numbers

Autor:	James A. Sellers, Arthur T. Benjamin, Sean S. Plott
Rok vydání:	2008
Předmět:	Combinatorics Mathematics::Combinatorics Proofs involving the addition of natural numbers Mathematics::History and Overview Bijection Discrete Mathematics and Combinatorics Mathematical proof Pell number Mathematics
Zdroj:	Annals of Combinatorics. 12:271-278
ISSN:	0219-3094 0218-0006
DOI:	10.1007/s00026-008-0350-5
Popis:	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.
Databáze:	OpenAIRE
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