Mathematical Sciences: Combinatorial Designs and Matrices

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This award supports the research of Professor Richard Wilson at The California Institute of Technology. It is a three year continuing grant made by the Algebra and Number Theory Program in the Division of Mathematical Sciences. Professor Wilson is one of the most innovative researchers in the area of mathematics known as combinatorial designs. His current research involves the decompositions of edge-colored complete graphs. Many standard combinatorial problems are easily reduced to this problem including the triple whist tournaments of E. H. Moore, nested triple systems and self-orthogonal Latin Squares. In this proposal he will continue the existence theory of the decomposition of these edge-colored graphs, generalizing his celebrated existence theory for pairwise balanced designs. Many important results can be expected from the research in this proposal.