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Combinatorial Proofs of Various q-Pell Identities via 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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References

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, North Georgia College and State University, 82 College Circle, Dahlonega, GA, 30597, USA

    Karen S. Briggs

  2. Department of Mathematics, Pennsylvania State University, University Park, State College, PA, 16802, USA

    David P. Little & James A. Sellers

Authors
  1. Karen S. Briggs
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  2. David P. Little
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  3. James A. Sellers
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Correspondence to Karen S. Briggs.

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Briggs, K.S., Little, D.P. & Sellers, J.A. Combinatorial Proofs of Various q-Pell Identities via Tilings. Ann. Comb. 14, 407–418 (2010). https://doi.org/10.1007/s00026-011-0067-8

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  • DOI: https://doi.org/10.1007/s00026-011-0067-8

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