On three-dimensional \(q\)-Riordan arrays

DOI10.1515/dema-2024-0005MaRDI QIDQ6590328

Gang Fang, Waseem Ahmad Khan, Ömer Duran, Nese Omur, Sibel Koparal

Publication date: 21 August 2024

Published in: Demonstratio Mathematica (Search for Journal in Brave)

zbMATH Keywords

generating functions\(q\)-binomial coefficientsthree-dimensional matrices\(q\)-Riordan arrays

Mathematics Subject Classification ID

(q)-calculus and related topics (05A30) Binomial coefficients; factorials; (q)-identities (11B65) Matrices, determinants in number theory (11C20)

Cites Work

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• The group of multi-dimensional Riordan arrays
• Identities induced by Riordan arrays
• The Riordan group
• An extension of the generalized Pascal matrix and its algebraic properties
• Generating trees and proper Riordan arrays
• \(q\)-Riordan representation
• Generalized harmonic numbers with Riordan arrays
• On identities involving generalized harmonic, hyperharmonic and special numbers with Riordan arrays
• $q$-Riordan array for $q$-Pascal matrix and its inverse matrix
• Riordan matrices and sums of harmonic numbers
• The linear algebra of the generalized Pascal matrix

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