Mathematical Sciences: Block Designs and Related Combinatorial Structures

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This award supports the research in combinatorial design theory and graph theory of Professor Charles Lindner of Auburn University. The emphasis of Dr. Lindner's research will be on problems in small embeddings of partial graph decompositions, the existence problem of 2-perfect decompositions of the complete graph into cycles, and the conjugate invariant subgroup problem for both orthogonal and perpendicular arrays. This research falls in the broad category of combinatorics, which is one of the most active fields in today's mathematics. Fundamentally, combinatorics represents a systematization of the very first of all mathematical activities, counting. In its modern development, however, combinatorics has gone beyond just counting to make use of a wide variety of advanced mathematical techniques, and although its roots go back several centuries, the field has had an explosive development in the past few decades because of its importance in communications and information technology.