On three-dimensional <i>q</i>-Riordan arrays-Reference-Cited by-同舟云学术

On three-dimensional q-Riordan arrays

Published:2024-01-01 Issue:1 Volume:57 Page:
ISSN:2391-4661
Container-title:Demonstratio Mathematica
language:en
Short-container-title:

Author:

Fang Gang¹,Koparal Sibel²,Ömür Neşe³,Duran Ömer³,Khan Waseem Ahmad⁴

Affiliation:

1. Institute of Computing Science and Technology, Guangzhou University , Guangzhou 510006 , China

2. Department of Mathematics, Bursa Uludağ University , Bursa 16059 , Türkiye

3. Department of Mathematics, Kocaeli University , Kocaeli 41380 , Türkiye

4. Department of Mathematics and Natural Sciences, Prince Mohammad Bin Fahd University , P.O. Box 1664 , Al Khobar 31952 , Saudi Arabia

Abstract

Abstract In this article, we define three-dimensional q-Riordan arrays and q-Riordan representations for these arrays. Also, we give four cases of infinite multiplication three-dimensional matrices of these arrays. As applications, we obtain three-dimensional

-Pascal-like matrix and its inverse matrix by Heine’s binomial formula, using combinatorial identities. Finally, we consider the generalization of three-dimensional

-Pascal-like matrix and give some identities involving

-binomial coefficients.

Publisher

Walter de Gruyter GmbH

Link

https://www.degruyter.com/document/doi/10.1515/dema-2024-0005/pdf

Reference20 articles.

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