Abstract
In Chapter 16, we studied different combinatorial models for Pell and Pell–Lucas polynomials by constructing linear and circular tilings of boards with n cells. In each case, our success hinged on a clever assignment of weights to square tiles and dominoes. Since the Pell family is a sub-family of the Chebyshev family, we are tempted to ask whether the Pell tiling models can be extended to the larger family. Fortunately, the answer is yes. We will begin our investigation with the Chebyshev tiling models for the polynomials U n (x) of the second kind.
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A.T. Benjamin and D. Walton, Counting on Chebyshev Polynomials, Mathematics Magazine 82 (2009), 117–126.
L.W. Shapiro, A Combinatorial Proof of a Chebyshev Polynomial Identity, Discrete Mathematics 34 (1981), 203–206.
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Koshy, T. (2014). Chebyshev Tilings. In: Pell and Pell–Lucas Numbers with Applications. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-8489-9_20
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DOI: https://doi.org/10.1007/978-1-4614-8489-9_20
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Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4614-8488-2
Online ISBN: 978-1-4614-8489-9
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