Some combinatorial identities via k-order Fibonacci matrices
- Cahit Köme,
Nevsehir Haci Bektas Veli University, Department of Mathematics, Nevsehir, Turkey,
Matrix factorizations have been widely used in recent years, especially in engineering problems, to facilitate performance-requiring computations. In this paper, we investigate some interesting relationships between some combinatorial matrices such as Pascal matrix, Stirling matrices and k-order Fibonacci matrix. We give factorizations and inverse factorizations of the Pascal and Stirling matrices via k-order Fibonacci matrix. Moreover, we derive various combinatorial properties by using relationships between these matrices. Finally, compared to previous studies, we present more general results for specific values of k.
Vol. 23 (2022), No. 1, pp. 281-294