Mathematical Sciences: Graph Designs and Generalized Embeddings

该奖项支持罗杰教授从事组合学的研究。罗杰教授将继续他在部分图设计的图分解和嵌入领域的研究。罗杰教授还将继续他对拉丁方的自然概括的发展，他称之为花纹孔。这种图案孔的概念导致了各种部分图设计的嵌入方面的显著改进，并导致了几个经典嵌入定理的推广。这项研究属于组合学的一般领域。组合学试图找到有效的方法来研究如何组织离散的集合。离散系统的行为对于现代通信来说是极其重要的。例如，大型网络的设计，如电话系统，以及计算机科学中的算法设计，都涉及离散对象，这利用了组合研究。

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.