Geodesic
\(q\)-Eulerian polynomials and polynomials with only real zeros
The electronic journal of combinatorics, Tome 15 (2008)
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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.
DOI : 10.37236/741
Classification : 05A15, 26C10 
@article{10_37236_741,
     author = {Shi-Mei Ma and Yi Wang},
     title = {\(q\)-Eulerian polynomials and polynomials with only real zeros},
     journal = {The electronic journal of combinatorics},
     year = {2008},
     volume = {15},
     doi = {10.37236/741},
     zbl = {1180.05009},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/741/}
}
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Shi-Mei Ma; Yi Wang. \(q\)-Eulerian polynomials and polynomials with only real zeros. The electronic journal of combinatorics, Tome 15 (2008). doi: 10.37236/741

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