On Operators on Polynomials Preserving Real-Rootedness and the Neggers-Stanley Conjecture

Authors:
Petter Brändén
Affiliations:
Matematik, Chalmers Tekniska Högskola Och Göteborgs Universitet, S-412 96 Göteborg, Sweden. branden@math.chalmers.se
Venue:
Journal of Algebraic Combinatorics: An International Journal
Year:
2004

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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 Hadamard 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.