q-almost Riordan arrays

Alp Y., Baran F. Y., Kocer G., TUĞLU N.

Filomat, vol.40, no.8, pp.3043-3059, 2026 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 40 Issue: 8
  • Publication Date: 2026
  • Doi Number: 10.2298/fil2608043a
  • Journal Name: Filomat
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Page Numbers: pp.3043-3059
  • Keywords: almost-Riordan arrays, q-analogue, Riordan arrays
  • Gazi University Affiliated: Yes

Abstract

Our focus is on examining a group of Riordan arrays in which each member is represented by a triple of power series that is called an almost-Riordan array. If we take a triple of power series that is chosen as a q-function, we identify the q-analogue of the almost-Riordan arrays called q-almost Riordan arrays. In addition, we obtain the fundamental theorem for q-almost Riordan arrays (FTqARA). For suitably chosen pairs of q-almost Riordan arrays, new formulas for the multiplication of any q-almost Riordan arrays are obtained. Finally, with the help of the FTqARA, the generating functions for some row sums of q-almost Riordan matrices are derived.