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arXiv · 2008.01480

Some Properties of a Class of Sparse Polynomials

Karl Dilcher·Maciej Ulas
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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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Karl Dilcher, Maciej Ulas. 2020-08-04. Some Properties of a Class of Sparse Polynomials. https://arxiv.org/abs/2008.01480

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