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.
