Zeros of rank-generating functions of Cohen-Macaulay complexes Original Research Article

Many combinatorial polynomials are related to rank-generating functions of Cohen-Macaulay complexes; notable among these are reliability, chromatic, flow, Birkhoff, and order polynomials. We prove two analytic theorems on the location of zeros of polynomials which have direct applications to the rank-generating functions of Cohen-Macaulay complexes and discuss their consequences for each of the aforementioned classes of polynomials.