Structure in designs, coverings and decompositions

组合设计提供了一种理想的方法来理解复杂离散结构（例如网络）的交互属性；一种研究此类结构的“互连性”特性的方法。 拟议研究计划的中心重点是对组合设计结构的研究；考虑具有特定结构或缺乏特定结构的设计。该领域的发展将提供对所涉及对象的结构的更深入的理解以及对其他组合问题的洞察。设计在统计、编码理论和调度方面有着众所周知的应用，此外，在算法效率、软件和网络测试以及数值分析等不同问题上也有潜在的应用。我长期以来一直致力于寻找各种类型的因式分解，最初是统一的和类统一的可解析设计，并将这项工作扩展到包括更一般的因式分解，尤其是循环因式分解。我还考虑了无法进行因式分解的情况。最近，我对覆盖数组产生了兴趣。该项目将支持我在所有这些领域的工作。

Combinatorial Designs provide an ideal way to understand the interaction properties of complex discrete structures, such as networks; a way to investigate the `interconnectedness' properties of such structures. The central focus of the proposed research program is the investigation of the structure of combinatorial designs; to consider designs with a particular structure, or lack thereof. Development in this area will provide a deeper understanding of the structure of the objects involved as well as insight into other combinatorial questions. Designs have well-known applications to statistics, coding theory and scheduling, in addition, there are potential applications to such diverse questions as algorithmic efficiency, software and network testing and numerical analysis. I have long been involved with finding various kinds of factorizations, initially uniform and class-uniformly resolvable designs, broadening this work to include more general factorizations, most notably cycle factorizations. I have also considered cases where factorization is not possible. More recently, I have become interested in Covering Arrays. This project will support my work in all of these areas.