Structure in designs, coverings and decompositions

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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.