给定行和与列和的矩阵计数

The Number of Matrices Given Sum of Row and Columns

利用方程组的理论,将有限域上给定行和向量与列和向量的阶的非负整数矩阵的个数问题,转化成求线性方程组解的问题。并给出了所有满足条件的矩阵。

In this paper,we give a formula for the number of matrices with given sum of rows and columns over finite field.Furthermore,we give the explicit form to these matrices.The method in this paper is elementary.At first the problem is reduced to equalities over finite field,then get all the results by solving these equalities.