RUI: Algebraic and Enumerative Combinatorics

Curtis Greene和Lynne Butler将继续研究代数和枚举组合学中的问题，特别强调离散结构（如偏置集、格和表）在经典群表示理论中的作用以及对称函数的相应问题。格林将重点研究具有非交换类似物的对称函数族的组合学和表示理论。Butler将继续她在Hall多项式上的工作，研究一些正多边形面格的有序类似物，并研究Macdonald的两变量Kostka函数的组合性质。这项研究属于组合学的一般领域。组合学试图找到有效的方法来研究离散的对象集合如何排列。离散系统的行为对现代通信极为重要。例如，大型网络的设计，例如在电话系统中出现的设计，以及计算机科学中处理离散对象集的算法设计，这就利用了组合研究。

Curtis Greene and Lynne Butler will continue their research into problems in algebraic and enumerative combinatorics, with special emphasis on the role of discrete structures such as posets, lattices, and tableaux in the representation theory of classical groups and corresponding problems for symmetric functions. Greene will focus on the combinatorics and representation theory underlying certain families of symmetric functions which have non-commutative analogues. Butler will continue her work on Hall polynomials, investigate the order analogues of face lattices of some regular polytopes, and study combinatorial properties of Macdonald's two-variable Kostka functions. This research is in the general area of Combinatorics. Combinatorics attempts to find efficient methods to study 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 thus 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.