On operators on polynomials preserving real-rootedness and the neggers-stanley conjecture

Abstract

We refine a technique used in a paper by Schur on real-rooted polynomials, This amounts to an extension of a theorem of Wagner on Hudamard products of Pólya frequency sequences. We also apply our results to polynomials for which the Neggers-Stanley Conjecture is known to hold. More precisely, we settle interlacing properties for E-polynomials of series-parallel posets and column-strict labelled Ferrers posets.