Some properties of a class of sparse polynomials |
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Authors: | Karl Dilcher Maciej Ulas |
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Institution: | 1. Department of Mathematics and Statistics, Dalhousie University, Halifax, Nova Scotia, B3H 4R2, Canada;2. Jagiellonian University, Faculty of Mathematics and Computer Science, Institute of Mathematics, ?ojasiewicza 6, 30-348 Kraków, Poland |
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Abstract: | We study an infinite class of sequences of sparse polynomials that have binomial coefficients both as exponents and as coefficients. This generalizes a sequence of sparse polynomials which arises in a natural way as graph theoretic polynomials. After deriving some basic identities, we obtain properties concerning monotonicity and log-concavity, as well as identities involving derivatives. We also prove upper and lower bounds on the moduli of the zeros of these polynomials. |
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Keywords: | Polynomial Monotonicity log-concavity Differential-difference equation Zero distribution |
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