Mathematical Sciences: Graph Designs and Generalized Embeddings

该奖项支持罗杰教授的研究工作， 在组合学中。 罗杰教授将继续他的 对图分解领域的研究， 部分图设计的嵌入。 罗杰教授还将 继续他对拉丁文的自然概括的发展 他称之为图案化的洞。 的这种圣贤观 图案化的孔导致了嵌入的戏剧性的改进， 各种部分图设计并导致了 几个经典的嵌入定理。 该研究是在组合学的一般领域。 组合数学试图找到有效的方法来研究如何 可以组织离散的集合。 离散的行为 系统对于现代通信是极其重要的。 为 例如，大型网络的设计，如电话系统， 计算机科学中的算法设计都涉及到 离散的物体，这就利用了组合研究。

This award supports the research of Professor Rodger to work in combinatorics. Professor Rodger will continue his investigations into the area of graph decompositions and embeddings of partial graph-designs. Professor Rodger will also continue his development of a natural generalization of latin squares, which he has called patterned holes. This concept of patterned holes has led to dramatic improvements in embeddings of various partial graph designs and has led to generalizations of several classical embedding theorems. The research is in the general area of combinatorics. Combinatorics attempts to find efficient methods to study how discrete collections can be organized. The behavior of discrete systems is extremely important to modern communications. For example, the design of large networks, as in telephone systems, and the design of algorithms in computer science all deal with discrete objects, and this makes use of combinatorial research.