一类稀疏多项式的若干性质
Some Properties of a Class of Sparse Polynomials
摘要：
我们研究了一类稀疏多项式序列的无穷大类，它们的系数和指数都是二项式系数。这推广了一系列稀疏多项式，其中出现在一个自然的方式作为图论多项式。在得到一些基本恒等式后，我们得到了单调性和对数单调性的性质，以及涉及导数的恒等式。我们还证明了这些多项式的零点模的上界和下界。
英文摘要：
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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