Mathematical Sciences: Research in Enumerative Combinatorics

这个奖项支持了Gessel在列举组合学的几个领域的问题上的研究。所有这些都涉及母函数方法的应用，要么是解决计数问题，要么是研究有理数序列。要研究的主题是二叉树、非交换对称函数、Rook理论、具有非负幂级数系数的有理函数和广义Dedekind和。这项研究属于组合学的一般领域。组合学的目标之一是找到有效的方法来研究离散的对象集合如何排列。离散系统的行为对于现代通信来说是极其重要的。例如，大型网络的设计，如那些发生在电话系统中的网络，以及计算机科学中的算法设计，都涉及离散的对象集，这利用了组合研究。

Gessel This award supports the investigations of Gessel on problems in several areas of enumerative combinatorics. All involve applications of the method of generating functions, either to solve counting problems or to study sequence of rational numbers. The topics to be studied are binary trees, noncommutative symmetric functions, rook theory, rational functions with nonnegative power series coefficients, and generalized Dedekind sums. This research is in the general area of Combinatorics. One of the goals of Combinatorics is to find efficient methods of studying how discrete collections of objects can be arranged. The behavior of discrete systems is extremely important to modern communications. For example, the design of large networks, such as those occurring in telephone systems, and the design of algorithms in computer science deal with discrete sets of objects, and this makes use of combinatorial research.