A unified approach to polynomial sequences with only real zeros

Details A unified approach to polynomial sequences with only real zeros A unified approach to polynomial sequences with only real zeros

2005-09-09

arxiv.org/abs/math/0509207v5

Advances in Applied Mathematics, 38 (2007) 542-560

Mathematics

Combinatorics

19 pages, Advances in Applied Mathematics, in press

Scientific paper

10.1016/j.aam.2006.02.003

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.

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