Mathematical Sciences: Algebraic Combinatorics

数学科学：代数组合

• 批准号: 9500979
• 负责人: Philip Hanlon
• 金额: $ 24.15万
• 依托单位: Regents of the University of Michigan - Ann Arbor
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-06-01 至 2001-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9500979&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Algebraic; Combinatorics

This award supports the research of Professor Philip Hanlon in the field of algebraic combinatorics. Hanlon will investigate a number of problems connected with two distinct subjects, the Macdonald Root System Conjectures and the inner product matrices defined by Varchenko in his work on representations of quantum groups and hypergeometric functions related to quantum groups. 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 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.

该奖项支持Philip Hanlon教授在代数组合学领域的研究。汉伦将调查一些问题与两个不同的主题，麦克唐纳根系猜想和内积矩阵定义的瓦尔琴科在他的工作表示的量子群和超几何函数有关的量子群。 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，如电话系统中的网络设计，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。