Identities via Bell matrix and Fibonacci matrix

Abstract

In this paper, we study the relations between the Bell matrix and the Fibonacci matrix, which provide a unified approach to some lower triangular matrices, such as the Stirling matrices of both kinds, the Lah matrix, and the generalized Pascal matrix. To make the results more general, the discussion is also extended to the generalized Fibonacci numbers and the corresponding matrix. Moreover, based on the matrix representations, various identities are derived.

Some Special Matrices and Combinatorial Identities

“…olacak şekilde = ( ) ve = ( ) matrisleri tanımlanır (Wang, 2008). şeklinde çarpanlarına ayrılabilir (Wang,2008).…”

On the involutions of the Riordan group

“…Recently the Riordan group has been used to obtain sequence identities. For example, in [7] the authors rewrote a combinatorially interesting element (g, f ) ∈ R by a product of two elements to obtain sequence identities.…”

A contribution to the connections between Fibonacci numbers and matrix theory

“…Various properties of these matrices and their generalizations have been studied, e.g. [1,2,6]. Another interesting connection is given in [3], where it is shown that the maximal determinant of an n × n (0,1)-Hessenberg matrix is F n .…”