Mathematical Sciences: The Combinatorics of Symmetric Functions

数学科学：对称函数的组合

• 批准号: 9306427
• 负责人: Jeffrey Remmel
• 金额: $ 6.51万
• 依托单位: University of California-San Diego
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1993
• 资助国家: 美国
• 起止时间: 1993-07-01 至 1996-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9306427&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Combinatorics; Symmetric; Functions

9306427 Remmel This award supports the research of Professor Remmel to work in combinatorics. Professor Remmel will continue his research into the combinatorics of symmetric functions. First, Professor Remmel plans to develop the combinatorics of the Macdonald polynomials and then he plans to study the action Macdonald operators on various bases of symmetric functions. Next, Professor Remmel plans to study the computation of Kronecker products and plethysms for the symmetric group and the hyperoctahedral group. 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. ***

9306427 REMMEL该奖项支持Remmel教授的研究，以合作。 Remmel教授将继续他对对称功能的组合学的研究。 首先，Remmel教授计划开发麦克唐纳多项式的组合，然后他计划在对称功能的各个基础上研究麦克唐纳运营商。 接下来，Remmel教授计划研究对称组和二十六面体群体的Kronecker产品和杂质的计算。 该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收集。 离散系统的行为对于现代通信非常重要。 例如，大型网络的设计，如电话系统中，计算机科学中的算法设计都涉及离散的对象，这利用了组合研究。 ***