$q$-Eulerian Polynomials and Polynomials with Only Real Zeros

  • Shi-Mei Ma
  • Yi Wang

Abstract

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 Brändén about the $q$-Eulerian polynomials.

Published
2008-01-21
Article Number
R17