Ma, Shi-Mei; Wang, Yi \(q\)-Eulerian polynomials and polynomials with only real zeros. (English) Zbl 1180.05009 Electron. J. Comb. 15, No. 1, Research Paper R17, 9 p. (2008). Summary: Let \(f\) and \(F\) be two polynomials satisfying \(F(x)=u(x)f(x)+v(x)f^{\prime}(x)\). 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 F. Brenti [“Unimodal, log-concave and Pólya frequency sequences in combinatorics”, Mem. Am. Math. Soc. 413 (1989; Zbl 0697.05011)] and P. Brändén [“On linear transformations preserving the Pólya frequency property”, Trans. Am. Math. Soc. 358, No.8, 3697–3716 (2006; Zbl 1086.05007)] about the \(q\)-Eulerian polynomials. Cited in 13 Documents MSC: 05A15 Exact enumeration problems, generating functions 26C10 Real polynomials: location of zeros Citations:Zbl 0697.05011; Zbl 1086.05007 PDFBibTeX XMLCite \textit{S.-M. Ma} and \textit{Y. Wang}, Electron. J. Comb. 15, No. 1, Research Paper R17, 9 p. (2008; Zbl 1180.05009) Full Text: arXiv EuDML EMIS