与Pell数相关的三角矩阵的一些组合性质

Some Combinatorial Properties of Triangu-lar Matrices Related to Pell Numbers

Pell数,记,本文主要研究由v(n,k)构成的三角矩阵以及其伴随三角矩阵的组合性质,包括:行多项式的实根性和稠密性,矩阵的渐近正态性以及全正性。

Pell number , denote . This article studies the combina-torial proprieties of two triangular matrices, one is formed by v(n,k) and the other is the adjoin-ing triangular matrices . More precisely we study the real rootedness and density of the row polynomials, and the asymptotic normality and total positivity of the matrices.