交换加法幂等半环上的矩阵积和式

研究交换加法幂等半环上矩阵及其伴随矩阵,得到若干积和式的性质,给出了伴随矩阵积和式的两个等式。本文的有些结论推广了模糊矩阵,格矩阵,坡矩阵上的相应结论。     

坡矩阵的积和式算子及若干不等式

引入坡矩阵积和式算子的概念．获得坡矩阵积和式算子关于偏序“≤”的若干不等式．     

(0,1)-矩阵的积和式的图表示及其相关性质

将(0，1)．矩阵的积和式的记数问题转化为它的伴随图或伴随有向图上相关元素的记数问题，能使复杂的计数问题变得相对直观化和简单化．本文给出了(0，1)-矩阵的积和式的图论表达式，并以该表达式为基础，主要解决了2．正则图类的邻接矩阵的最大积和式的记数问题以及它的反问题，即确定了零积和式临界图的极大边数及其图类．     

积和式及行列式的一个推广

基于对积和式性质的讨论,给出了积和式的"化长为方"计算方法;基于对积和式概念的研究,作为行列式的推广,给出了一般m×n矩阵的行式定义,讨论了行式的性质和计算方法,推广了克莱姆法则.     

一类(0,1)-矩阵的最大积和式

本文给出了每条线恰有n-2个1的n阶(0.1)-矩阵的最大积和式的组合表达式.     

涉及正定矩阵的一些函数的凸性及其应用

利用张量积的性质以及关于矩阵酉不变范数的两个不等式,研究了涉及正定矩阵的几个映射及函数的凸性,通过所得结果得到了关于矩阵迹、积和式及广义矩阵函数的一些不等式,并给出其在量子信息论中的一些应用.     

一类(0,1)-矩阵的最大积和式的积分表达式

给出了线和n-2的n阶（0，1）－矩阵的最大积和式的积分表达式，并证明了该积分表达式与[1]得到的组合表达式等价。     

积和式的一个性质

<正> 数域F上所有n×m矩阵的集合记为M_(n×m)(F),数域F上所有n阶方阵的集合记为M_n(F).设A=(a_(ii))∈M_n(F).方阵A的积和式(permanent)记为perA,它定义为     

GCD矩阵的一种推广

本文研究了有限个正整数直积上的GCD矩阵.利用Mbius反演得到了直积上的GCD矩阵性质和GCD矩阵行列式的计算方法.进一步,把正整数直积上的GCD矩阵推广到一般偏序集直积上,得到了广义GCD矩阵的性质.     

关于积和式的几个等式

本文主要讨论积和式几个等式,并得到部分结果.     

Computing permanents via determinants for some classes of sparse matrices

Starting from recent formulas for calculating the permanents of some sparse circulant matrices, we obtain more general formulas expressing the permanents of a wider class of matrices as a linear combination of appropriate determinants.     

Minimum Permanents of Tridiagonal Doubly Stochastic Matrices

We determine the minimum permanents and minimizing matrices of the tridiagonal doubly stochastic matrices and of certain doubly stochastic matrices with prescribed zero entries.     

Minimum Permanents of Tridiagonal Doubly Stochastic Matrices

We determine the minimum permanents and minimizing matrices of the tridiagonal doubly stochastic matrices and of certain doubly stochastic matrices with prescribed zero entries.     

Permanents and determinants with generic noncommuting entries

This paper studies some basic combinatorial properties of matrix functions of generic matrices. A generic matrix is one with entries from a free associative algebra, over a field, and on a finite set of non-commuting variables (i.e. a tensor algebra). The principal tools are shuffle products. Generic column and row permanents are defined and analogs of the Laplace and Cauchy-Binet theorems are derived in terms of shuffles. In this setting, the generic permanents include as special cases all of the classical matrix functions: Schur matrix functions, determinants, and permanents. 1980 Mathematics Classification 05, 15. Keywords: Shuffle product, generic matrix functions, minor expansions, Laplace Expansion Theorem, Cauchy-Binet Theorem, permanents, determinants, tensor algebra, matrices with non-commuting entries.     

Limit theorems for random permanents with exchangeable structure

Permanents of random matrices extend the concept of U-statistics with product kernels. In this paper, we study limiting behavior of permanents of random matrices with independent columns of exchangeable components. Our main results provide a general framework which unifies already existing asymptotic theory for projection matrices as well as matrices of all-iid entries. The method of the proofs is based on a Hoeffding-type orthogonal decomposition of a random permanent function. The decomposition allows us to relate asymptotic behavior of permanents to that of elementary symmetric polynomials based on triangular arrays of rowwise independent rv's.     

Bounds for permanents and determinants

An inequality of Johnson and Newman for determinants of real matrices is extended to complex matrices. A related inequality for permanents of real matrices is improved by means of a new rearrangement theorem.     

Permanents of doubly stochastic matrices

A conjecture on the permanents of doubly stochastic matrices is proposed. Some results supporting it are presented.     

Permanental ideals of Hankel matrices

We provide the Gröbner basis and the primary decomposition of the ideals generated by 2 × 2 permanents of Hankel matrices.     

Minimum Permanents on a Face of the Polytope of Doubly Stochastic Matrices II

We determine the minimum permanents and minimizing matrices on the face of z_3+n, for the fully indecomposable (0,1) matrices of order 3+n, which include an identity submatrix of order n .