Mathematical Sciences: Study of Association Schemes and Their Character Tables

数学科学：关联方案及其特征表的研究

• 批准号: 8904972
• 负责人: Eiichi Bannai
• 金额: --
• 依托单位: Ohio State University Research Foundation -DO NOT USE
• 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 1990-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8904972&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Study; Association; Schemes

This award supports the research in Algebraic Combinatorics of Professor Eiichi Bannai of Ohio State University. He will study P- and Q-polynomial association schemes, distance-regular graphs and digraphs, and general commutative association schemes of large class number. His research emphasizes the interplay of algebraic combinatorics with the theory of finite groups, with the theory of orthogonal polynomials, and with various representation theories, including the representation theory of classical and Chevalley groups. 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.

该奖项支持俄亥俄州立大学 Eiichi Bannai 教授的代数组合学研究。他将研究P-和Q-多项式关联方案、距离正则图和有向图，以及大类数的一般交换关联方案。他的研究强调代数组合学与有限群理论、正交多项式理论以及各种表示理论（包括经典群和谢瓦莱群的表示理论）的相互作用。 这项研究属于组合数学的广泛范畴，它是当今数学中最活跃的领域之一。 从根本上说，组合学代表了所有数学活动中最重要的活动——计数的系统化。然而，在其现代发展中，组合学已经超越了单纯的计数，而是利用了各种先进的数学技术，尽管其根源可以追溯到几个世纪前，但由于其在通信和信息技术中的重要性，该领域在过去几十年中取得了爆炸性的发展。