Doubly stochastic matrices and the Bruhat order

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• 作者：Richard A. Brualdi ; Geir Dahl ; Eliseu Fritscher
• 关键词：Bruhat order ; doubly stochastic matrix ; face
• 刊名：Czechoslovak Mathematical Journal
• 出版年：2016
• 出版时间：September 2016
• 年：2016
• 卷：66
• 期：3
• 页码：681-700
• 全文大小：212 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Analysis
  Convex and Discrete Geometry
  Ordinary Differential Equations
  Mathematical Modeling and IndustrialMathematics
  
• 出版者：Springer Netherlands
• ISSN：1572-9141
• 卷排序：66

文摘

The Bruhat order is defined in terms of an interchange operation on the set of permutation matrices of order n which corresponds to the transposition of a pair of elements in a permutation. We introduce an extension of this partial order, which we call the stochastic Bruhat order, for the larger class Ω_n of doubly stochastic matrices (convex hull of n×n permutation matrices). An alternative description of this partial order is given. We define a class of special faces of Ω_n induced by permutation matrices, which we call Bruhat faces. Several examples of Bruhat faces are given and several results are presented.