Abstract
We assemble our toolbox from real and complex analysis. The main topics are inequalities inspired by convexity, polynomials with no roots in a particular domain and relations between convexity and restrictions on the location of the roots. We discuss the entropy of partitions, the Bethe-entropy, the Prékopa–Leindler inequality for integrals and the capacity of polynomials with non-negative real coefficients as a way to estimate a particular coefficient of a multivariate polynomial by solving a convex optimization problem.
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© 2016 Springer International Publishing AG
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Barvinok, A. (2016). Preliminaries. In: Combinatorics and Complexity of Partition Functions. Algorithms and Combinatorics, vol 30. Springer, Cham. https://doi.org/10.1007/978-3-319-51829-9_2
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DOI: https://doi.org/10.1007/978-3-319-51829-9_2
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Publisher Name: Springer, Cham
Print ISBN: 978-3-319-51828-2
Online ISBN: 978-3-319-51829-9
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