Corpus ID: 49324478

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}
}
• Alexander I. Barvinok
• Published 2018
• Mathematics, Computer Science
• ArXiv
• 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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