Mathematical Sciences: Research in Enumerative Combinatorics

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This award supports the research of Professor Gessel to work in enumerative combinatorics related to lattice paths, permutations, and symmetric functions. Many of these problems deal with methods for counting objects, which are in general very difficult problems. The problem related to lattice paths involves counting nonintersecting paths according to the number of left-hand and right -hand turns, and finding a combinatorial interpretation to some generalizations of the ballot numbers. 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.