Polynomials with the half-plane property and the support theorems
A multivariate polynomial has the half-plane property whenever it has no roots when all variables have positive real part. Extending an earlier theorem that the support of every homogeneous multiaffine polynomial forms the set of bases of a matroid, the paper establishes a condition ensuring that the support forms a jump system (a generalization of matroids); this condition is that all terms in the polynomial have the same parity. Connections to the location of the roots of reliability polynomials are explored.
scientific article; zbMATH DE number 2165071