The \(q\)-log-convexity of the Narayana polynomials of type \(B\)

DOI10.1016/j.aam.2009.03.004zbMath1230.05276OpenAlexW2021347618MaRDI QIDQ846216

Arthur L. B. Yang, William Y. C. Chen, Larry X. W. Wang, Robert L. Tang

Publication date: 2 February 2010

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

Full work available at URL: https://doi.org/10.1016/j.aam.2009.03.004

zbMATH Keywords

Schur positivity\(q\)-log-convexityNarayana numbers of type \(B\)Pieri's ruleprincipal specializationthe Jacobi-Trudi identity

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Symmetric functions and generalizations (05E05) Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.) (33D45)

Related Items (22)

On a Stirling-Whitney-Riordan triangle ⋮ Polynomials related to \(q\)-analog of the generalized derivative polynomials ⋮ Some positivities in certain triangular arrays ⋮ \(q\)-log-convexity from linear transformations and polynomials with only real zeros ⋮ A generalized ordered Bell polynomial ⋮ Positivity of Iterated Sequences of Polynomials ⋮ Log-convexity and strong \(q\)-\(\log\)-convexity for some triangular arrays ⋮ A planar network proof for Hankel total positivity of type \(B\) Narayana polynomials ⋮ Linear transformations preserving the strong \(q\)-log-convexity of polynomials ⋮ 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 ⋮ Proofs of some conjectures on monotonicity of number-theoretic and combinatorial sequences ⋮ Narayana polynomials and Hall-Littlewood symmetric functions ⋮ 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 ⋮ A generalized Eulerian triangle from staircase tableaux and tree-like tableaux ⋮ Positivity and continued fractions from the binomial transformation ⋮ Two integer sequences related to Catalan numbers ⋮ Log-Concavity of Combinations of Sequences and Applications to Genus Distributions

Uses Software

• Maple
• SF
• ACE

Cites Work

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• Schur positivity and the \(q\)-log-convexity of the Narayana polynomials
• On the q-log-concavity of Gaussian binomial coefficients
• Reduced matrices and q-log-concavity properties of q-Stirling numbers
• Growth series of finite extensions of \(Z^ n \)are rational
• Inductive proofs of \(q\)-log concavity
• Non-crossing partitions for classical reflection groups
• A Maple package for symmetric functions
• Combinatorial statistics on type-B analogues of noncrossing partitions and restricted permutations
• A note on log-convexity of \(q\)-Catalan numbers
• On the log-convexity of combinatorial sequences
• The q-log-concavity of q-binomial coefficients
• Recurrence Relations for Strongly q-Log-Convex Polynomials
• Root Polytopes and Growth Series of Root Lattices

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