Iterated sequences and the geometry of zeros

DOI10.1515/CRELLE.2011.063zbMath1278.30007arXiv0909.1927OpenAlexW3105580025MaRDI QIDQ3094347

Petter Brändén

Publication date: 24 October 2011

Published in: Journal für die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0909.1927

zbMATH Keywords

conjecture of Boros and Mollconjecture of Fisk, McNamara-Sagan and Stanleyinfinitely log-concave sequences

Mathematics Subject Classification ID

Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) (30C15) Real polynomials: analytic properties, etc. (26C05)

Related Items (29)

Infinite log-concavity for polynomial Pólya frequency sequences ⋮ Descent generating polynomials and the Hermite-Biehler theorem ⋮ Positivity of Toeplitz determinants formed by rising factorial series and properties of related polynomials ⋮ Positivity of Iterated Sequences of Polynomials ⋮ Laguerre inequalities for discrete sequences ⋮ Higher-order interlacing for matrix-valued meromorphic Herglotz functions ⋮ Longest increasing subsequences and log concavity ⋮ Higher order Turán inequalities for Boros-Moll sequences ⋮ Brenti's Open Problem on the Real-Rootedness of $q$-Eulerian Polynomials of Type $D$ ⋮ Derivation of the real-rootedness of coordinator polynomials from the Hermite-Biehler theorem ⋮ A simple proof of higher order Turán inequalities for Boros-Moll sequences ⋮ A unified approach to multivariate polynomial sequences with real stability ⋮ The unimodality of a polynomial coming from a rational integral. Back to the original proof ⋮ On the concavity properties of certain arithmetic sequences and polynomials ⋮ Properties arising from Laguerre-Pólya class for the Boros-Moll numbers ⋮ Nonnegative minors of minor matrices ⋮ Higher order log-concavity in Euler's difference table ⋮ Unnamed Item ⋮ The concavity and convexity of the Boros-Moll sequences ⋮ The real-rootedness of generalized Narayana polynomials related to the Boros-Moll polynomials ⋮ On the KNS conjecture in type \(E\) ⋮ THE LOCAL -POLYNOMIALS OF CLUSTER SUBDIVISIONS HAVE ONLY REAL ZEROS ⋮ A proof of the Shepp-Olkin entropy monotonicity conjecture ⋮ An inequality for coefficients of the real-rooted polynomials ⋮ Log-convex and Stieltjes moment sequences ⋮ The Zagier modification of Bernoulli numbers and a polynomial extension. I ⋮ Higher order Turán inequalities for the partition function ⋮ Hankel-total positivity of some sequences ⋮ On multiple and infinite log-concavity

Cites Work

• Infinite log-concavity: developments and conjectures
• A Computer Proof of Moll’s Log-Concavity Conjecture
• On sequences of polynomials and the distribution of their zeros

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