Mathematical Sciences: Graph Designs and Related Combinatorial Structures

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This award supports the research of Professor Lindner to work in combinatorics. The objective of this proposal is basic research in graph designs and related combinatorial structures. In particular, the investigator intends to place emphasis on problems dealing with small embeddings for a pair of orthogonal latin squares and continued generalizations on embeddings latin squares and rectangles. 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.