In this paper, two kinds of generalized Pascal matrices Pn,k and Qn,k, and two kinds of generalized Pascal functional matrices On,k[x,y] and Qn,k[x,y] are introduced and studied. Factorization of Pascal matrices into ...In this paper, two kinds of generalized Pascal matrices Pn,k and Qn,k, and two kinds of generalized Pascal functional matrices On,k[x,y] and Qn,k[x,y] are introduced and studied. Factorization of Pascal matrices into products of (0,1) Jordan matrices is established. Factorization of Pascal functional matrices into products of bidiagonal matrices is obtained.展开更多
Summetor is an operator used in the mathematics to calculate the special numbers like binomial coefficients and combinations of group elements. It has many applications in algebra, matrices like calculation of pascal ...Summetor is an operator used in the mathematics to calculate the special numbers like binomial coefficients and combinations of group elements. It has many applications in algebra, matrices like calculation of pascal triangle elements and pascal matrix formation, etc. This paper explains about its functions and properties of N-Summet-k. The result of variation between N and k is shown in tabulation.展开更多
In this paper,using the Jordan canonical form of the Pascal matrix Pn,we present a new approach for inverting the Pascal matrix plus a scalar Pn+aIn for arbitrary real number a≠1.
In this paper, we consider <i>r</i>-generalization of the central factorial numbers with odd arguments of the first and second kind. Mainly, we obtain various identities and properties related to these num...In this paper, we consider <i>r</i>-generalization of the central factorial numbers with odd arguments of the first and second kind. Mainly, we obtain various identities and properties related to these numbers. Matrix representation and the relation between these numbers and Pascal matrix are given. Furthermore, the distributions of the signless r-central factorial numbers are derived. In addition, connections between these numbers and the Legendre-Stirling numbers are given.展开更多
EI-Mikkawy M obtained that the symmetric Pascal matrix Qn and the Vandermonde matrix Vn are connected by the equation Qn= TnVn, where Tn is a stochastic matrix in [1]. In this paper, a decomposition of the matrix Tn i...EI-Mikkawy M obtained that the symmetric Pascal matrix Qn and the Vandermonde matrix Vn are connected by the equation Qn= TnVn, where Tn is a stochastic matrix in [1]. In this paper, a decomposition of the matrix Tn is given via the Stirling matrix of the first kind, and a recurrence relation of the elements of the matrix T, is obtained, so an open urnblem urouosed bv EI-Mikkawv[2] is solved. Some combinatorial identities are also given.展开更多
基金Development Program for Outstanding Young Teachers in Lanzhou University of Technology(Q02018)
文摘In this paper, two kinds of generalized Pascal matrices Pn,k and Qn,k, and two kinds of generalized Pascal functional matrices On,k[x,y] and Qn,k[x,y] are introduced and studied. Factorization of Pascal matrices into products of (0,1) Jordan matrices is established. Factorization of Pascal functional matrices into products of bidiagonal matrices is obtained.
文摘Summetor is an operator used in the mathematics to calculate the special numbers like binomial coefficients and combinations of group elements. It has many applications in algebra, matrices like calculation of pascal triangle elements and pascal matrix formation, etc. This paper explains about its functions and properties of N-Summet-k. The result of variation between N and k is shown in tabulation.
基金Supported by the Natural Science Foundation of Gansu Proveince（1010RJZA049）
文摘In this paper,using the Jordan canonical form of the Pascal matrix Pn,we present a new approach for inverting the Pascal matrix plus a scalar Pn+aIn for arbitrary real number a≠1.
文摘In this paper, we consider <i>r</i>-generalization of the central factorial numbers with odd arguments of the first and second kind. Mainly, we obtain various identities and properties related to these numbers. Matrix representation and the relation between these numbers and Pascal matrix are given. Furthermore, the distributions of the signless r-central factorial numbers are derived. In addition, connections between these numbers and the Legendre-Stirling numbers are given.
基金the NSF of Gansu Province of China (3ZS041-A25-007)
文摘EI-Mikkawy M obtained that the symmetric Pascal matrix Qn and the Vandermonde matrix Vn are connected by the equation Qn= TnVn, where Tn is a stochastic matrix in [1]. In this paper, a decomposition of the matrix Tn is given via the Stirling matrix of the first kind, and a recurrence relation of the elements of the matrix T, is obtained, so an open urnblem urouosed bv EI-Mikkawv[2] is solved. Some combinatorial identities are also given.
