Remarks and open problems on the minimum permanent of acyclic doubly stochastic matrices

被引：1

作者：

da Fonseca, C. M. ^{[1
]}

机构：

[1] Univ Coimbra, Dept Math, P-3001454 Coimbra, Portugal

来源：

LINEAR & MULTILINEAR ALGEBRA | 2013年 / 61卷 / 03期

关键词：

permanent; doubly stochastic matrices; Birkhoff polytope; trees; second largest eigenvalue; cohesive (0,1)-matrix; barycentric (0,1)-matrix; fastest mixing Markov chain; MIXING MARKOV-CHAIN; POLYTOPE; FACES; CONJECTURE; IDENTITY;

D O I：

10.1080/03081087.2012.675332

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We formulate several open problems and conjectures involving acyclic doubly stochastic matrices with minimum permanent and the minimum second largest eigenvalue. New characterizations and illustrative examples of these permanental minimizing matrices are provided in this article. In addition, we show that the adjacency matrix of any tree, with more than 2 vertices, plus the identity matrix is not cohesive.

引用

页码：281 / 293

页数：13

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