Zeros of Multivariate Polynomials in Combinatorics
Abstract.
Zeros of univariate polynomials in combinatorics, and
related notions such as unimodality and log-concavity have been
studied for a long time. In particular, several important polynomials
in combinatorics are known to have only real zeros. Recently a theory
around a generalization of real-rooted polynomials to several
variables has been developed and used to solve problems in
combinatorics and other areas of mathematics. We will survey this
method, with particular focus on combinatorial aspects.