Stability of combinatorial polynomials and its applications

Abstract

Many important problems are closely related to the zeros of certain polynomials derived from combinatorial objects. The aim of this paper is to make a systematical study on the stability of polynomials in combinatorics.Applying the characterizations of Borcea and Brändén concerning linear operators preserving stability, we present criteria for real stability and Hurwitz stability of recursive polynomials. We also give a criterion for Hurwitz stability of the Turán