Turkish Journal of Mathematics
Abstract
In this study, we introduce the concept of a bi-Riordan array. As part of this construction, we define new composition and power operations. We then establish an analogue of the well-known fundamental theorem of Riordan arrays (FTRA), which we call the fundamental theorem of bi-Riordan arrays. Next, we show that the product of two bi-Riordan matrices is again a bi-Riordan matrix. Using this product structure, we prove that the set of bi-Riordan matrices forms a monoid.
DOI
10.55730/1300-0098.3778
Keywords
Riordan arrays, generating functions, bi-Riordan arrays
First Page
989
Last Page
1007
Publisher
The Scientific and Technological Research Council of Türkiye (TÜBİTAK)
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
Recommended Citation
TUĞLU, N, & YEŞİL BARAN, F (2026). Characterizations of bi-Riordan arrays. Turkish Journal of Mathematics 50 (5): 989-1007. https://doi.org/10.55730/1300-0098.3778
