Recurrence matrices

Determinants related to Dirichlet characters modulo 2, 4 and 8 of binomial coefficients and the algebra of recurrence matrices

Using recurrence matrices, defined and described with some details, we study a few determinants related to evaluations of binomial coefficients on Dirichlet characters modulo 2, 4 and 8.

带状Toeplitz矩阵行列式与积和式的构造性递推

Constructive recurrences for determinants and permanents of banded Toeplitz matrices

针对带状Toeplitz矩阵，提出两种构造性Laplace展开方法，得到行列式与积和式的极小阶递推，并精确分类状态图，推广至循环情形。

Evaluations of some determinants of matrices related to the Pascal triangle

We prove several evaluations of determinants of matrices, the entries of which are given by the recurrence $a_{i,j}=a_{i-1,j}+a_{i,j-1}$, or variations thereof. These evaluations were either conjectured or extend conjectures by Roland Bacher [J. Théorie Nombres Bordeaux 13 (2001), to appear; see http://arxiv.org/abs/math.CO/0109013].

A few remarks on Euler and Bernoulli polynomials and their connections with binomial coefficients and modified Pascal matrices

We prove certain identities involving Euler and Bernoulli polynomials that can be treated as recurrences. We use these and also other known identities to indicate connection of Euler and Bernoulli numbers with entries of inverses of certain lower triangular built of binomial coefficients. Another words we interpret Euler and Bernoulli numbers in terms of modified Pascal matrices.

多项式序列的线性化与连接系数：一种矩阵方法

Linearization and connection coefficients of polynomial sequences: A matrix approach

本研究采用矩阵方法，推导多项式序列线性化系数与连接系数的显式表达式及递推关系，并将结果应用于正交多项式序列及切比雪夫、埃尔米特、沙利耶等具体正交多项式族。