A unified approach to polynomial sequences with only real zeros
Combinatorics
2010-08-17 v5
Abstract
We give new sufficient conditions for a sequence of polynomials to have only real zeros based on the method of interlacing zeros. As applications we derive several well-known facts, including the reality of zeros of orthogonal polynomials, matching polynomials, Narayana polynomials and Eulerian polynomials. We also settle certain conjectures of Stahl on genus polynomials by proving them for certain classes of graphs, while showing that they are false in general.
Cite
@article{arxiv.math/0509207,
title = {A unified approach to polynomial sequences with only real zeros},
author = {Lily L. Liu and Yi Wang},
journal= {arXiv preprint arXiv:math/0509207},
year = {2010}
}
Comments
19 pages, Advances in Applied Mathematics, in press