Combinatorial Proofs of Various q-Pell Identities via Tilings

Karen S. Briggs; David P. Little; James A. Sellers

doi:10.1007/s00026-011-0067-8

Combinatorial Proofs of Various q-Pell Identities via Tilings

Karen S. Briggs, David P. Little, James A. Sellers

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

Recently, Benjamin, Plott, and Sellers proved a variety of identities involving sums of Pell numbers combinatorially by interpreting both sides of a given identity as enumerators of certain sets of tilings using white squares, black squares, and gray dominoes. In this article, we state and prove q-analogues of several Pell identities via weighted tilings.

Original language	English (US)
Pages (from-to)	407-418
Number of pages	12
Journal	Annals of Combinatorics
Volume	14
Issue number	4
DOIs	https://doi.org/10.1007/s00026-011-0067-8
State	Published - Dec 2010
Externally published	Yes

Keywords

Pell numbers
combinatorial identities
q-enumeration
tilings

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abstract = "Recently, Benjamin, Plott, and Sellers proved a variety of identities involving sums of Pell numbers combinatorially by interpreting both sides of a given identity as enumerators of certain sets of tilings using white squares, black squares, and gray dominoes. In this article, we state and prove q-analogues of several Pell identities via weighted tilings.",

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AU - Little, David P.

AU - Sellers, James A.

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KW - combinatorial identities

KW - q-enumeration

KW - tilings

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Combinatorial Proofs of Various q-Pell Identities via Tilings

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Keywords

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