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美国乔治亚州立大学数学与统计系李忠善教授应邀来我院做学术报告
2019-06-12 10:36     (访问量:)

 

学术报告通知

 

报告题目:Convex polytopes and minimum ranks of   nonnegative signpattern

                    matrices

报告人:李忠善教授  (美国乔治亚州立大学数学与统计系)

报告时间:619 日下午3-4

报告地点:数统院307      

 数学与统计学院

2019.06.12

   

 

 

报告摘要:A sign pattern matrix (resp., nonnegative sign patternmatrix) is a matrix whose entries are from the set $\{+, -, 0\}$ (resp., $ \{+, 0 \}$). The minimum rank (resp., rational minimum rank) of a  sign patternmatrix $\cal A$ is the minimum of the ranks of the  matrices (resp.,rational matrices) whose entries have signs equal to the corresponding entriesof $\cal A$. Using a correspondence between sign patterns with minimum rank$r\geq 2$ and  point-hyperplane configurations in $\mathbb R^{r-1}$ andSteinitz's theorem on the rational realizability of 3-polytopes, it is shownthat for every nonnegative sign pattern of minimum rank at most 4, the minimumrank and the rational minimum rank are equal. But there are nonnegative signpatterns with minimum rank 5 whose rational minimum rank is greater than5.  It is established that every $d$-polytope determines a nonnegativesign pattern with minimum rank $d+1$ that has a $(d+1)\times (d+1)$ triangular submatrix with all diagonal entries positive.  It is also shownthat  there are at most  $\min \{ 3m, 3n \}$ zero entries inany  condensed nonnegative $m \times n$ sign pattern of minimum rank 3.Some bounds on the entries of some integer matrices achieving the minimum ranksof nonnegative sign patterns with minimum rank 3 or 4 are established

 

报告人简介:李忠善,美国佐治亚州立大学数学系终身正教授。兰州大学数学学学士、北京师范大学硕士美国北卡罗来纳州立大学博士。研究兴趣包括组合矩阵理论、代数图论、矩阵理论应用等。

 

  

   

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