Mathematical Sciences: The Combinatorics of Symmetric Functions

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9306427 Remmel This award supports the research of Professor Remmel to work in combinatorics. Professor Remmel will continue his research into the combinatorics of symmetric functions. First, Professor Remmel plans to develop the combinatorics of the Macdonald polynomials and then he plans to study the action Macdonald operators on various bases of symmetric functions. Next, Professor Remmel plans to study the computation of Kronecker products and plethysms for the symmetric group and the hyperoctahedral group. 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. ***