Mathematical Sciences: Combinatorial Designs and Matrices

该奖项支持理查德·威尔逊教授的研究 在加州理工学院。 这是一个三年 代数和数论项目的持续资助， 数学科学部 威尔逊教授是最具创新精神的研究人员之一 在被称为组合设计的数学领域。 他 目前的研究涉及边缘着色的分解 完全图 许多标准的组合问题很容易 减少到这个问题，包括三重惠斯特锦标赛的 E. H.摩尔、套三元系与自正交拉丁 正方形 在这个提议中他将继续存在理论 这些边着色图的分解，推广 他著名的两两平衡设计存在理论。 这方面的研究可望取得许多重要成果。 提议

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.