Algebraic Combinatorics

代数组合学

• 批准号: 9401575
• 负责人: John Stembridge
• 金额: $ 10.25万
• 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: 1994
• 资助国家: 美国
• 起止时间: 1994-06-01 至 1998-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9401575&HistoricalAwards=false
• 关键词: Algebraic; Combinatorics

9401575 Stembridge This award funds the research of Professor John Stembridge into applications of combinatorial methods into problems of Algebra. The goal is to produce algorithmic methods for producing certain generating functions, enumerating reduced expressions obtained from studies of algebra, and constructing particular bases. The results should have applications in algebra, number theory and algebraic geometry. This research falls in the broad category of combinatorics, which is one of the most active fields in today's mathematics. At its roots, combinatorics is the study of systematic counting. Counting can be incredibly difficult when the objects are difficult to list, and combinatorists look for general methods for overcoming these difficulties. Today's combinatorics makes use of a wide variety of the most advanced and modern mathematical techniques. Although its roots go back several centuries, the field has had an explosive development in the past few decades. This growth comes from its importance in communications and information technology and from the success of modern techniques to problems of counting.

9401575 Stembridge该奖项资助John Stembridge教授将组合方法应用于代数问题的研究。其目标是产生算法方法来产生特定的生成函数，列举从代数研究中获得的简化表达式，并构造特定的基。这些结果应该在代数、数论和代数几何中有应用。这项研究属于组合学的广泛范畴，这是当今数学中最活跃的领域之一。从根本上说，组合学是对系统计数的研究。当对象很难列出时，计算可能会非常困难，组合学家寻找克服这些困难的一般方法。今天的组合学利用了各种各样最先进、最现代的数学技术。虽然它的起源可以追溯到几个世纪前，但在过去的几十年里，这一领域得到了爆炸性的发展。这一增长来自于它在通信和信息技术中的重要性，以及从现代技术的成功到计算问题。