Analysis of the structure of Latin Squares

Latin squares are core building blocks in combinatorics, and are used for designing experiments, schedules and erro-correcting codes. They also play a role in other mathematical disciplines such as algebra and finite geometry. Long-standing open problems concerning the existence of latin squares with certain properties illustrate the shorthfalls in our current understanding of these fudnamental combinatorial objects. his project will advance udnerstanding of the basic pieces from which latin squares are built, and use the new knowldge to construct latin squares with rare but desirable properties. In the process significant unsolved problems in the area will be resolved.