Briggs, Karen S.; Little, David P.; Sellers, James A. Combinatorial proofs of various \(q\)-Pell identities via tilings. (English) Zbl 1233.05037 Ann. Comb. 14, No. 4, 407-418 (2010). Summary: Recently, A.T. Benjamin, S.S. Plott, and J.A. Sellers [Ann. Comb. 12, No.3, 271–278 (2008; Zbl 1169.05305)] 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. Cited in 6 Documents MSC: 05A19 Combinatorial identities, bijective combinatorics 05B45 Combinatorial aspects of tessellation and tiling problems 05A15 Exact enumeration problems, generating functions 11B39 Fibonacci and Lucas numbers and polynomials and generalizations Keywords:Pell numbers; combinatorial identities; tilings; \(q\)-enumeration Citations:Zbl 1169.05305 PDFBibTeX XMLCite \textit{K. S. Briggs} et al., Ann. Comb. 14, No. 4, 407--418 (2010; Zbl 1233.05037) Full Text: DOI References: [1] Andrews G.E.: The Theory of Partitions. Addison-Wesley, Reading (1976) · Zbl 0371.10001 [2] Benjamin A.T., Plott S.P., Sellers J.A.: Tiling proofs of recent sum identities involving Pell numbers. Ann. Combin. 12(3), 271–278 (2008) · Zbl 1169.05305 · doi:10.1007/s00026-008-0350-5 [3] Santos J.P.O., Sills A.V.: q-Pell sequences and two identities of V. A. Lebesgue. Discrete Math. 257, 125–142 (2002) · Zbl 1007.05017 · doi:10.1016/S0012-365X(01)00475-7 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.