摘要
n+1阶下三角方阵Ln[x]定义为:(Ln[x])ij=(?)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)(k-j i-j)和 ,即二项式型多项式函数矩阵.n+1阶方阵Ln定义为:当i≥j时,(Ln)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Ln[x]与Ln,得到了更一般的结果和一些组合恒等式.
The properties of the lower triangular functional matrix Ln[x] associated with a polynomial of binomial type are discussed in this paper, in which the entry-(i,j) of Ln[x] is equal to lij =(?)i-j(x)l(i,j)if i≥j and equal to 0 otherwise, with l(i, k)l(k,j) = l(i,j)(k-j i-j) and for integers n,k,i,j and real numbers x,y. Pascal matrix and its generalizations are special cases of Ln[x]. More general results and some combinatorial identities are derived.
