Brenti's Open Problem on the Real-Rootedness of $q$-Eulerian Polynomials of Type $D$

DOI10.1137/16M1084651zbMath1366.05008OpenAlexW2618920110MaRDI QIDQ5346566

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Publication date: 24 May 2017

Published in: SIAM Journal on Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/16m1084651

zbMATH Keywords

descentRouth-Hurwitz stability criterion\(q\)-Eulerian polynomial of type \(D\)pairwise interlacing

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Real polynomials: location of zeros (26C10)

Related Items (3)

Some results related to Hurwitz stability of combinatorial polynomials ⋮ A unified proof of interlacing properties of eigenvalues of totally positive matrices ⋮ The converse of Weyl's eigenvalue inequality

Cites Work

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• The roots of the independence polynomial of a clawfree graph
• \(q\)-Eulerian polynomials arising from Coxeter groups
• Unimodality, log-concavity, real-rootedness and beyond
• Combinatorics of Coxeter Groups
• Iterated sequences and the geometry of zeros
• Zeros of Reliability Polynomials and f-vectors of Matroids
• The 𝐬-Eulerian polynomials have only real roots

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