Log-convexity and strong \(q\)-\(\log\)-convexity for some triangular arrays

DOI10.1016/j.aam.2012.11.003zbMath1277.05014OpenAlexW2055840522MaRDI QIDQ384940

Bao-Xuan Zhu

Publication date: 29 November 2013

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

Full work available at URL: https://doi.org/10.1016/j.aam.2012.11.003

zbMATH Keywords

\(\log\)-convexity\(q\)-\(\log\)-convexity2-order total positivitystrong \(q\)-\(\log\)-convavitystrong \(q\)-\(\log\)-convexity

Mathematics Subject Classification ID

Determinants, permanents, traces, other special matrix functions (15A15) Combinatorial inequalities (05A20)

Related Items (35)

On a Stirling-Whitney-Riordan triangle ⋮ Some analytical properties of the matrix related to q-coloured Delannoy numbers ⋮ Recurrence relations for the linear transformation preserving the strong \(q\)-log-convexity ⋮ Polynomials related to \(q\)-analog of the generalized derivative polynomials ⋮ \(q\)-log-convexity from linear transformations and polynomials with only real zeros ⋮ Two-Motzkin-like numbers and Stieltjes moment sequences ⋮ Some polynomials related to Dowling lattices and \(\mathrm{x}\)-Stieltjes moment sequences ⋮ A generalized ordered Bell polynomial ⋮ Positivity of Iterated Sequences of Polynomials ⋮ A planar network proof for Hankel total positivity of type \(B\) Narayana polynomials ⋮ Linear transformations preserving the strong \(q\)-log-convexity of polynomials ⋮ Lattice Paths and Branched Continued Fractions: An Infinite Sequence of Generalizations of the Stieltjes–Rogers and Thron–Rogers Polynomials, with Coefficientwise Hankel-Total Positivity ⋮ Some positivities in Stirling arrays with higher level ⋮ Some results related to Hurwitz stability of combinatorial polynomials ⋮ \(Q\)-total positivity and strong \(q\)-log-convexity for some generalized triangular arrays ⋮ Context-free grammars, generating functions and combinatorial arrays ⋮ Total positivity of some polynomial matrices that enumerate labeled trees and forests. I: Forests of rooted labeled trees ⋮ Analytic aspects of generalized central trinomial coefficients ⋮ Immanant positivity for Catalan-Stieltjes matrices ⋮ The Laguerre-Pólya class and combinatorics. Abstracts from the workshop held March 13--19, 2022 ⋮ The Monotonicity and Log-Behaviour of Some Functions Related to the Euler Gamma Function ⋮ Lattice paths and branched continued fractions. II: Multivariate Lah polynomials and Lah symmetric functions ⋮ Proofs of some conjectures on monotonicity of number-theoretic and combinatorial sequences ⋮ The Euler and Springer numbers as moment sequences ⋮ Total positivity of recursive matrices ⋮ On total positivity of Catalan-Stieltjes matrices ⋮ Log-convex and Stieltjes moment sequences ⋮ Strong \(q\)-log-convexity of the Eulerian polynomials of Coxeter groups ⋮ A combinatorial proof of the log-convexity of sequences in Riordan arrays ⋮ Stieltjes moment properties and continued fractions from combinatorial triangles ⋮ Log-convexity of Aigner-Catalan-Riordan numbers ⋮ A generalized Eulerian triangle from staircase tableaux and tree-like tableaux ⋮ Positivity and continued fractions from the binomial transformation ⋮ Zeros distribution of the reverse strong Turán expressions of polynomials sequences ⋮ Total Positivity from the Exponential Riordan Arrays

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unimodality problems of multinomial coefficients and symmetric functions
• Schur positivity and the \(q\)-log-convexity of the Narayana polynomials
• The \(q\)-log-convexity of the Narayana polynomials of type \(B\)
• Reduced matrices and q-log-concavity properties of q-Stirling numbers
• On unimodality problems in Pascal's triangle
• Combinatorial aspects of continued fractions
• Inductive proofs of \(q\)-log concavity
• Some \(q\)-analogues of the Schröder numbers arising from combinatorial statistics on lattice paths
• Catalan-like numbers and determinants
• On the average rank of an element in a filter of the partition lattice
• Polynomials with real zeros and Pólya frequency sequences
• Enumerative aspects of secondary structures
• Combinatorics and total positivity
• Log-concavity and related properties of the cycle index polynomials
• A unified approach to polynomial sequences with only real zeros
• A note on log-convexity of \(q\)-Catalan numbers
• Enumeration via ballot numbers
• On the log-convexity of combinatorial sequences
• Logarithmic behavior of some combinatorial sequences
• A note on concavity properties of triangular arrays of numbers
• The q-log-concavity of q-binomial coefficients
• Recurrence Relations for Strongly q-Log-Convex Polynomials
• Eulerian polynomials as moments, via exponential Riordan arrays
• Log Concave Sequences of Symmetric Functions and Analogs of the Jacobi-Trudi Determinants
• Addition theorems via continued fractions
• Motzkin numbers

This page was built for publication: Log-convexity and strong \(q\)-\(\log\)-convexity for some triangular arrays