$q$-Eulerian polynomials and polynomials with only real zeros

Details $q$-Eulerian polynomials and polynomials with only real zeros $q$-Eulerian polynomials and polynomials with only real zeros

2006-11-27

arxiv.org/abs/math/0611826v2

The Electronic Journal of Combinatorics 15 (2008) #R17

Mathematics

Combinatorics

8 pages, minor corrections

Scientific paper

Let $f$ and $F$ be two polynomials satisfying $F(x)=u(x)f(x)+v(x)f'(x)$. We
characterize the relation between the location and multiplicity of the real
zeros of $f$ and $F$, which generalizes and unifies many known results,
including the results of Brenti and Br\"and\'en about the $q$-Eulerian
polynomials.

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