Generalized Bell Numbers and Peirce Matrix via Pascal Matrix

The Generalized Pascal Matrix via the Generalized Fibonacci Matrix and the Generalized Pell Matrix

In [4], the authors studied the Pascal matrix and the Stirling matrices of the first kind and the second kind via the Fibonacci matrix. In this paper, we consider generalizations of Pascal matrix, Fibonacci matrix and Pell matrix. And, by using Riordan method, we have factorizations of them. We, also, consider some combinatorial identities.

Identities via Bell matrix and Fibonacci matrix

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, ba...

Generalized Near-Bell Numbers

The nth near-Bell number, as defined by Beck, enumerates all possible partitions of an n-multiset with multiplicities 1, 1, 1, . . . , 1, 2. In this paper we study the sequences arising from a generalization of the near-Bell numbers, and provide a method for obtaining both their exponential and their ordinary generating functions. We derive various interesting relationships amongst both the gen...

An involutory Pascal matrix

An involutory upper triangular Pascal matrix Un is investigated. Eigenvectors of Un and of UT n are considered. A characterization of Un is obtained, and it is shown how the results can be extended to matrices over a commutative ring with unity. © 2004 Elsevier Inc. All rights reserved.

Generalized Pascal k-eliminated functional matrix with 2n variables