Topics in combinatorial matrix theory

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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.