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

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 21 Jan 2008Embargo end date: 01 Jan 2006Publisher:The Electronic Journal of CombinatoricsJournal:The Electronic Journal of Combinatorics, volume 15 (eissn: 1077-8926,

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Authors: Shi-Mei Ma; Yi Wang;

doi: 10.37236/741 , 10.48550/arxiv.math/0611826

arXiv: math/0611826

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

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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.

Related Organizations

Dalian Polytechnic University
China (People's Republic of)

Keywords

05A20, 26C10, Exact enumeration problems, generating functions, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), Real polynomials: location of zeros

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