Mathematical Sciences: Latin Squares, Block Designs, and Related Combinatorial Structures

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The objective of this project is basic research in combinatorial mathematics covering such topics as latin squares, quasigroups, block designs, graph decomposition problems and related combinatorial structures. Heavy emphasis will be placed on the conjugate invariant subgroup problem for both orthogonal and perpendicular arrays, Mendelsohn and Steiner pentagon systems, and various types of graph decomposition problems. Combinatorial mathematics is the study of various problems concerning finite sets. These problems have become very important because of their great applicability to computer research and in the design of statistical experiments.