The University of Michigan Combinatorics Seminar
A multivariate polynomial has the half-plane property if it is non-zero whenever all variables have positive real parts. In a recent paper, Choe, Oxley, Sokal and Wagner proved that the support of a homogeneous multi-linear polynomial with the half-plane property is the set of bases of a matroid. They also raised the question if this can be generalized so that the support of any multivariate polynomial with the half-plane property is a jump system. A jump system is a generalization of matroids. We answer this question to the affirmative and if time permits we will talk about other features of polynomials with the half-plane property.