On three-dimensional q-Riordan arrays

被引：0

作者：

Fang, Gang ^{[2
]}

Koparal, Sibel ^{[3
]}

Omur, Nese ^{[1
]}

Duran, Omer ^{[1
]}

Khan, Waseem Ahmad ^{[4
]}

机构：

[1] Kocaeli Univ, Dept Math, TR-41380 Kocaeli, Turkiye

[2] Guangzhou Univ, Inst Comp Sci & Technol, Guangzhou 510006, Peoples R China

[3] Bursa Uludag Univ, Dept Math, TR-16059 Bursa, Turkiye

[4] Prince Mohammad Bin Fahd Univ, Dept Math & Nat Sci, POB 1664, Al Khobar 31952, Saudi Arabia

来源：

DEMONSTRATIO MATHEMATICA | 2024年 / 57卷 / 01期

基金：

中国国家自然科学基金;

关键词：

q-Riordan arrays; three-dimensional matrices; q-binomial coefficients; generating functions; PASCAL MATRIX; NUMBERS;

D O I：

10.1515/dema-2024-0005

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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 q-Pascal-like matrix and its inverse matrix by Heine's binomial formula, using combinatorial identities. Finally, we consider the generalization of three-dimensional q-Pascal-like matrix and give some identities involving q-binomial coefficients.

引用

页数：12

共 46 条

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[3] Production Matrices and Riordan Arrays
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[9] Sequence characterization of almost-Riordan arrays
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[10] LEVEL GENERATING TREES AND PROPER RIORDAN ARRAYS
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