Mathematical Sciences: Algebraic Combinatorics: Permutations and Partially Ordered Sets

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This award supports the research of Professor C. Greene to work in combinatorics. He intends to investigate partially ordered sets, representations of the symmetric group and tableaux. In particular, he intends to work on Young's seminormal representation of the symmetric group, Mobius functions on planar lattices, balanced tableaux, the lattice of shuffles and a conjecture of D. Jackson on lattice-determinants. The research is in the general area of combinatorics. Combinatorics attempts to find efficient methods to study how discrete collections of objects can be organized. And, so it 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.