Some combinatorial identities via k-order Fibonacci matrices

Abstract

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 matrices. We give factorizations and inverse factorizations of the Pascal and Stirling matrices via k-order Fibonacci matrices. 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