On three-dimensional <i>q</i>-Riordan arrays

Fang G., KOPARAL S., ÖMÜR N., Duran O., Khan W. A.

DEMONSTRATIO MATHEMATICA, sa.1, 2024 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Basım Tarihi: 2024
  • Doi Numarası: 10.1515/dema-2024-0005
  • Dergi Adı: DEMONSTRATIO MATHEMATICA
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Linguistic Bibliography, zbMATH, Directory of Open Access Journals
  • Kocaeli Üniversitesi Adresli: Evet

Özet

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.