Mathematical Sciences: Research in Enumerative Combinatorics

该奖项支持Gessel教授在与点阵路径、排列和对称函数相关的枚举组合学方面的研究。这些问题中有许多涉及对象计数的方法，这通常是非常困难的问题。与点阵路径相关的问题包括根据左向和右向转弯的次数来计算不相交的路径，并找到对选票号码的一些概括的组合解释。这项研究是在组合学的一般领域。组合学试图找到有效的方法来研究如何组织离散集合。离散系统的行为对现代通信极为重要。例如，大型网络的设计，如电话系统，以及计算机科学中算法的设计都涉及离散对象，这就利用了组合研究。

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.