Mathematical Sciences: Algebraic Combinatorics

数学科学：代数组合

• 批准号: 8903246
• 负责人: Philip Hanlon
• 金额: $ 19.23万
• 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: 1989
• 资助国家: 美国
• 起止时间: 1989-06-01 至 1993-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8903246&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Algebraic; Combinatorics

This award supports the research in Combinatorics of Professor Philip Hanlon of the University of Michigan at Ann Arbor. Dr. Hanlon will work in two general problem areas at the junction of Combinatorics and Representation Theory. The first area is concerned with the homology of certain nilpotent Lie algebras, and homological extensions to the Macdonald root- system conjectures. The second area is concerned with problems related to Jones's basic construction, and the algebra structures of Brauer's centralizer algebras corresponding to Stanley's Fibonacci r-differential posets. This research falls in the broad category of Combinatorics, which is one of the most active fields in today's mathematics. Fundamentally, Combinatorics represents a systematization of the very first of all mathematical activities, counting. In its modern development, however, Combinatorics has gone beyond just counting to make use of a wide variety of advanced mathematical techniques, and although its roots go back several centuries, the field has had an explosive development in the past few decades because of its importance in communications and information technology.

该奖项支持组合数学的研究， 密歇根大学安分校的菲利普·汉伦教授 杆.汉伦博士将在两个一般问题领域的工作， Combinatorics和Representation Theory的交叉点。第一 面积是关于某些幂零李的同调 代数，和同调扩展的麦克唐纳根- 系统配置第二个方面是有关问题 与琼斯的基本结构有关， Brauer的中心化代数对应于Stanley的 Fibonacci r-微分偏序集 这项研究福尔斯属于组合学的大范畴， 这是当今数学中最活跃的领域之一。 从根本上说，组合数学代表了一个系统化的 首先是数学活动，计数在其 然而，现代的发展，组合数学已经不仅仅是 计数利用各种先进的数学 技术，虽然它的根源可以追溯到几个世纪， 在过去的几十年里， 因为它在通信和信息方面的重要性， 技术.