# Approximating real-rooted and stable polynomials, with combinatorial applications

@article{Barvinok2018ApproximatingRA, title={Approximating real-rooted and stable polynomials, with combinatorial applications}, author={Alexander I. Barvinok}, journal={ArXiv}, year={2018}, volume={abs/1806.07404} }

Let $p(x)=a_0 + a_1 x + \ldots + a_n x^n$ be a polynomial with all roots real and satisfying $x \leq -\delta$ for some $0 0$. Consequently, if $m_k(G)$ is the number of matchings with $k$ edges in a graph $G$, then for any $0 0$ is an absolute constant. We prove a similar result for polynomials with complex roots satisfying $\Re\thinspace z \leq -\delta$ and apply it to estimate the number of unbranched subgraphs of $G$.

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