RUI: Algebraic and Enumerative Combinatorics

RUI：代数和枚举组合学

• 批准号: 9500962
• 负责人: Curtis Greene
• 金额: $ 15.68万
• 依托单位: Haverford College
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-06-01 至 1998-10-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9500962&HistoricalAwards=false
• 关键词: RUI; Algebraic; Enumerative; Combinatorics

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.

柯蒂斯格林和林恩巴特勒将继续他们的研究问题的代数和枚举组合，特别强调离散结构的作用，如偏序集，格，并tableaux在代表理论的经典群体和相应的问题对称函数。格林将专注于组合学和代表性理论的基础上某些家庭的对称功能，其中有非交换类似物。巴特勒将继续她的工作霍尔多项式，调查的顺序类似物的面格的一些定期多面体，并研究组合性质的麦克唐纳的两个变量Kostka功能。 这项研究是在组合数学的一般领域。 组合数学试图找到有效的方法来研究如何安排离散的对象集合。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，如电话系统中的设计，以及计算机科学中的算法设计，都要处理离散的对象集，这就需要使用组合研究。