具有二项式型多项式下三角矩阵的性质

The Properties of Lower Triangular Matrix Associated with Polynomial of Binomial Type

中文关键词:  Pascal矩阵  二项式型多项式  下三角矩阵

英文关键词:Pascal matrix  polynomial of binomial type  lower triangular matrix

中文摘要:

      n+1阶下三角方阵L_n[x]定义为:(L_n[x])_ij=φ_i-j(x)l(i,j)(如果i≥j),否则为0,且满足条件l(i,k)l(k,j)=l(i,j)(i-j k-j)和(?),即二项式型多项式函数矩阵.n+1阶方阵L_n定义为:当i≥j时,(L_n)_ij=l(i,j),否则为0.本文研究了比Pascal函数矩阵及Lah矩阵更广泛的一类矩阵L_n[x]与L_n,得到了更一般的结果和一些组合恒等式.

英文摘要:

      The properties of the lower triangular functional matrix L_n[x] associated with a polynomial of binomial type are discussed in this paper, in which the entry-(i,j) of L_n[x] is equal to l_ij =φ_i-j(x)l(i,j)if i≥j and equal to 0 otherwise, with l(i, k)l(k,j) = l(i,j)(i-j k-j) and (?) for integers n,k,i,j and real numbers x,y. Pascal matrix and its generalizations are special cases of L_n[x]. More general results and some combinatorial identities are derived.