Topics in combinatorial matrix theory

组合矩阵理论与服务于学术界和工业界的几个数学领域相互作用。这些理论包括图论、组合设计和编码理论。图论被管理人员用于时间安排，被计算机科学家用于机器架构和网络的设计，被化学家用于分子模型。组合设计用于设计新产品（如药物、杀虫剂和植物品种）有效性的统计测试。编码理论用于有效地存储和传输数字数据，例如在计算机、光盘和卫星广播中。我的一些学生（主要是学士或硕士）进入了工业或国防领域。我所有的博士生都在大学或学院担任职务，并将他们的职业生涯奉献给了研究和/或培训。与过去一样，这项资助的工作是纯理论的，强调培养研究生和博士后。

Combinatorial matrix theory interacts with several areas of mathematics that serve the academic andindustrial communities.  These include graph theory, combinatorial designs and coding theory.  Graphtheory is used by managers for time scheduling, by computer scientists for the design of machinearchitectures and networks, and by chemists for molecular models.  Combinatorial designs are used todesign statistical tests for effectiveness of new products such as drugs, insecticides and plantvarieties.  Coding theory is used for efficient storage and transmission of digital data as in, forexample, computers, compact discs, and satellite broadcasts.Some of my students (mainly B.Sc. or M.Sc.) have gone into industry or national defense.  All of my Ph.D.students have positions in universities or colleges and have devoted their careers to research and/ortraining.  As in the past, the work proposed in this grant is purely theoretical and emphasizes trainingof graduate students and postdoctoral fellows.