Mathematical Sciences: Combinatorial Designs and Matrices

该奖项支持加州理工学院理查德·威尔逊教授的研究。它是由数学科学部的代数和数论项目提供的一项为期三年的持续资助。威尔逊教授是数学组合设计领域最具创新性的研究人员之一。他目前的研究涉及边缘彩色完全图的分解。许多标准的组合问题很容易归结为这个问题，包括E. H. Moore的三重惠斯特比赛、嵌套三重系统和自正交拉丁方。在这个建议中，他将继续这些边色图分解的存在理论，推广他著名的两两平衡设计的存在理论。在这个建议的研究中可以预期许多重要的结果。

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.