The limiting distribution of the coefficients of the 𝑞-Catalan numbers

DOI10.1090/S0002-9939-08-09464-1zbMath1146.05005arXiv0708.2574MaRDI QIDQ3532499

William Y. C. Chen, Carol J. Wang, Larry X. W. Wang

Publication date: 28 October 2008

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0708.2574

zbMATH Keywords

Bernoulli numbermoment generating functionunimodalitylog-concavity\(q\)-Catalan number

Mathematics Subject Classification ID

Combinatorial probability (60C05) Asymptotic enumeration (05A16)

Related Items (13)

The \(q\)-log-concavity and unimodality of \(q\)-Kaplansky numbers ⋮ The metric space of limit laws for $q$-hook formulas ⋮ On the distribution of the major index on standard Young tableaux ⋮ The \(q\)-Catalan numbers: a saddle point approach ⋮ Mahonian pairs ⋮ Asymptotic normality in t-stack sortable permutations ⋮ Asymptotic normality of the major index on standard tableaux ⋮ On parity unimodality of \(q\)-Catalan polynomials ⋮ An analytic proof of the Borwein conjecture ⋮ The asymptotic normality of adjacency coefficients of bipartite graphs and skew-adjacency coefficients of oriented graphs ⋮ A combinatorial proof of the parity unimodality of the \((m,n)\)-rational \(q\)-Catalan polynomial for \(m=3\) ⋮ Limit distribution of the coefficients of polynomials with only unit roots ⋮ Some limit properties for the coefficients of the \(q\)-Catalan numbers

Cites Work

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• q-Catalan numbers
• Catalan numbers, \(q\)-Catalan numbers and hypergeometric series
• Sharp bounds for the Bernoulli numbers
• Applications of q-Lagrange Inversion to Basic Hypergeometric Series
• A New q-Lagrange Formula and some Applications
• Probabilistic Methods in Combinatorial Analysis

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