## On operators on polynomials preserving real-rootedness and the Neggers-Stanley conjecture

##### J. Algebr. Comb. 20(2), 119-130 (2004)
DOI: 10.1023/B:JACO.0000047295.93525.df

### Summary

Summary: 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.

### Keywords/Phrases

neggers-Stanley conjecture, real-rooted polynomials, Sturm sequence