RUI: Algebraic and Enumerative Combinatorics

柯蒂斯·格林和林恩·巴特勒将继续研究代数和计数组合学中的问题，特别强调偏序集、格和表等离散结构在经典群的表示理论中的作用以及对称函数的相应问题。格林将专注于某些对称函数族背后的组合学和表示理论，这些函数族具有非对易类似物。巴特勒将继续她在霍尔多项式方面的工作，研究一些正则多面体的面格的序类似，并研究麦克唐纳的两个变量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。离散系统的行为对于现代通信来说是极其重要的。例如，大型网络的设计，例如在电话系统中发生的这种情况，以及计算机科学中的算法设计，都是处理离散的对象集，这利用了组合研究。

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.