Symmetric Pascal matrices modulo p

We study characteristic polynomials of symmetric matrices with entries ${i+j\choose i}$ the binomial coefficients, over finite fields.Comment: 16 pages, added reference, changes in presentation, correction of an error in a proo

Generalized Pascal functional matrix and its applications

AbstractIn this paper, we introduce the generalized Pascal functional matrix and show that the existing variations of Pascal matrices are special cases of this generalization. We study some algebraic properties of such generalized Pascal functional matrices. In addition, we demonstrate a direct application of these properties by deriving several novel combinatorial identities and a nontraditional approach for LU decompositions of some well-known matrices (such as symmetric Pascal matrices)

ON GENERALIZATIONS OF STIRLING NUMBERS AND SOME WELL-KNOWN MATRICES

We introduce a generalization of the Stirling numbers of the first kind and the second kind. By arranging these numbers into matrices, we generalize the Stirling matrices of the first kind and the second kind investigated by Cheon and Kim [Stirling matrix via Pascal matrix, Linear Algebra Appl. 329 (2001) 49–59]. Furthermore, we introduce generalizations of the Pascal matrix and the symmetric Pascal matrix with two real arguments, and generalize earlier results related to the Pascal matrices, Stirling matrices and matrices involving Bell numbers

On block matrices of pascal type in clifford analysis

Since the 90-ties the Pascal matrix, its generalizations and applications have been in focus of a great amount of publications. As it is well known, the Pascal matrix, the symmetric Pascal matrix and other special matrices of Pascal type play an important role in many scientific areas, among them Numerical Analysis, Combinatorics, Number Theory, Probability, Image processing, Sinal processing, Electrical enginneering, etc. We present a unified approach to matrix representations of special polynomials in several hypercomplex variables (new Bernoulli, Euler etc. polynomials), extending results of H. Malonek, G.Tomaz: Bernoulli polynomials and Pascal matrices in the context of Clifford Analysis, Discrete Appl. Math. 157(4) (2009) 838-847. The hypercomplex version of a new Pascal matrix with block structure, which resembles the ordinary one for polynomials of one variable will be discussed in detail