Infinite log-concavity: developments and conjectures

DOI10.1016/j.aam.2009.03.001zbMath1184.05005arXiv0808.1065OpenAlexW2154951927WikidataQ123258382 ScholiaQ123258382MaRDI QIDQ1036515

Peter R. W. McNamara, Bruce E. Sagan

Publication date: 13 November 2009

Published in: Advances in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0808.1065

zbMATH Keywords

computer proofsymmetric functionsToeplitz matricesbinomial coefficientsreal rootsGaussian polynomialinfinite log-concavity

Mathematics Subject Classification ID

Factorials, binomial coefficients, combinatorial functions (05A10) (q)-calculus and related topics (05A30) Symmetric functions and generalizations (05E05) Combinatorial inequalities (05A20) Iteration theory, iterative and composite equations (39B12) Basic hypergeometric functions (33D99)

Related Items (17)

Infinite log-concavity for polynomial Pólya frequency sequences ⋮ Schur positivity and the \(q\)-log-convexity of the Narayana polynomials ⋮ Positivity of Iterated Sequences of Polynomials ⋮ Longest increasing subsequences and log concavity ⋮ On the concavity properties of certain arithmetic sequences and polynomials ⋮ Geometric and functional inequalities for log-concave probability sequences ⋮ Nonnegative minors of minor matrices ⋮ 2-Log-Concavity of the Boros–Moll Polynomials ⋮ The real-rootedness of generalized Narayana polynomials related to the Boros-Moll polynomials ⋮ On the KNS conjecture in type \(E\) ⋮ Log-concavity of \(P\)-recursive sequences ⋮ An inequality for coefficients of the real-rooted polynomials ⋮ Log-convex and Stieltjes moment sequences ⋮ Higher order Turán inequalities for the partition function ⋮ Iterated sequences and the geometry of zeros ⋮ Hankel-total positivity of some sequences ⋮ Log-Concavity of Combinations of Sequences and Applications to Genus Distributions

Uses Software

• OEIS

Cites Work

• Confirming two conjectures of Su and Wang on binomial coefficients
• Unbounded regions of infinitely logconcave sequences
• On unimodality problems in Pascal's triangle
• q-Catalan numbers
• Total positivity of Hadamard products
• Probabilistic bounds on the coefficients of polynomials with only real zeros
• Polynomials with real zeros and Pólya frequency sequences
• \(q\)-Narayana numbers and the flag \(h\)-vector of \(J(\text \textbf{2}\times {\mathbf n})\)
• On a unimodal sequence of binomial coefficients
• On the generating functions of totally positive sequences. I
• Unimodal, log-concave and Pólya frequency sequences in combinatorics
• Matrix Analysis
• A Computer Proof of Moll’s Log-Concavity Conjecture
• On linear transformations preserving the Pólya frequency property
• Compressions of Totally Positive Matrices
• Bijective proofs for Schur function identities which imply Dodgson's condensation formula and Plücker relations
• Plücker relations on Schur functions
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