积和式性质定理及应用

摘要

组合矩阵论是近年兴起的1个数学分支。它通过矩阵论和线性代数来证明组合性定理；以及对组合结构进行描述和分类。为了更好地研究用矩阵来描述组合问题，引入矩阵的1个不变量—积和式。本第1部分是引言，在第2部分给出了矩阵积和式的定义及历史，积和式的1些基本性质，其中对积和式和行列式的1些性质做了比较；第3部分主要介绍了积和式中的Laplace定理等1些定理及证明；最后介绍了积和式的1些应用问题和广义积和式的概念，包括积和式在组合论、运筹学中的1些应用。

关键字:积和式；行列式； 0-1矩阵

Abstract

The theory of combination-matrix is a mathematic branch which emerges recent years . It proves the combinative theorem through theory of matrix and the linear algebra; and it also carries on the description and the classification to the built-up section. In order to studies well with the matrix to describes the combination question, it introduces a invariable of matrix---accumulates with the type. The first part is foreword, In the second part, this paper illustrates the definition and the history of the Permanent of matrix, and some basic characteristics of Permanent, including the comparison of Permanent and Determinant in some characteristics. In the third part,it mainly introduces the Laplace theorem and other theorems of Permanent and their proof. Finally it introduces some application questions of Permanent and the concept of the generalized Permanent, including the application of Permanent in combination- theory.

Keywords:Permanent； Determinant ；0-1 matrix