Isolated sets of diagonals, diagonal hypergraphs, and simplices of doubly stochastic matrices

被引：1

作者：

Brualdi, Richard A. ^{[1
]}

Shao, Jia-Yu ^{[2
]}

机构：

[1] Univ Wisconsin, Dept Math, Madison, WI 53706 USA

[2] Tongji Univ, Dept Appl Math, Shanghai 200092, Peoples R China

来源：

LINEAR & MULTILINEAR ALGEBRA | 2008年 / 56卷 / 04期

基金：

中国国家自然科学基金;

关键词：

matrix diagonal; isolated diagonals; doubly stochastic matrices; simplex; permanent; cohesive; barycentric;

D O I：

10.1080/03081080701437616

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We investigate a connection between isolated sets of diagonals of a matrix and simplicial faces of the polytope Omega(n) of doubly stochastic matrices. We also consider the minimum permanent on simplicial faces of Omega(n).

引用

页码：471 / 480

页数：10

共 9 条

[1]

Brualdi R A., 1985, Linear Multilinear Algebra, V17, P5, DOI [10.1080/03081088508817637, DOI 10.1080/03081088508817637]

[2] CONVEX POLYHEDRA OF DOUBLY STOCHASTIC MATRICES .1. APPLICATIONS OF PERMANENT FUNCTION [J].

BRUALDI, RA ;

GIBSON, PM .

JOURNAL OF COMBINATORIAL THEORY SERIES A, 1977, 22 (02) :194-230

[3] DIAGONAL HYPERGRAPH OF A MATRIX (BIPARTITE GRAPH) [J].

BRUALDI, RA .

DISCRETE MATHEMATICS, 1979, 27 (02) :127-147

[4] MATRICES WITH ISOMORPHIC DIAGONAL HYPERGRAPHS [J].

BRUALDI, RA ;

ROSS, JA .

DISCRETE MATHEMATICS, 1981, 33 (02) :123-138

[5] ON THE MINIMUM VALUE OF THE PERMANENT OF A NEARLY DECOMPOSABLE DOUBLY STOCHASTIC MATRIX [J].

FOREGGER, TH .

LINEAR ALGEBRA AND ITS APPLICATIONS, 1980, 32 (AUG) :75-85

[6]

HWANG SG, 1993, LINEAR MULTILINEAR A, V35, P313

[7]

McDonald JJ, 1997, LINEAR ALGEBRA APPL, V267, P359, DOI 10.1016/S0024-3795(97)80057-2

[8] Characterizations and applications of the isolated sets of permutations [J].

Shao, Jia-Yu ;

Ren, Ling-Zhi ;

Wu, Qun .

LINEAR & MULTILINEAR ALGEBRA, 2007, 55 (01) :45-56

[9] MINIMUM PERMANENTS ON CERTAIN FACES OF MATRICES CONTAINING AN IDENTITY SUBMATRIX [J].

SONG, SZ .

LINEAR ALGEBRA AND ITS APPLICATIONS, 1988, 108 :263-280

← 1 →