Larry Rolen

Affiliation: Vanderbilt University

Title Of Talk: Inequalities for the partition function and other combinatorial sequences

Abstract: The study of asymptotic properties of sequences is of fundamental interest in number theory and combinatorics. We are especially interested in proving inequalities among sequences of numbers. This topic has seen a large outpouring of work in recent years. For instance, Nicolas and DeSalvo–Pak independently proved that the partition function $p(n)$ is eventually log-concave. Specifically, they showed that $p^2(n)-p(n-1)p(n+1)\geq0$ for $n\geq 26$. Work of Griffin, Ono, Zagier, and myself placed this in a larger context by proving that related polynomial zero properties follow from a general phenomenon dictated by Hermite polynomials. In this talk, describing joint work with Koustav Banerjee and Kathrin Bringmann, I will present a unified framework to prove a wide class of inequalities of sequences.

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