Mathematical Sciences: Algebraic Combinatorics: Association Schemes and Related Topics

数学科学：代数组合：关联方案和相关主题

• 批准号: 8703075
• 负责人: Eiichi Bannai
• 金额: --
• 依托单位: Ohio State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1987
• 资助国家: 美国
• 起止时间: 1987-06-01 至 1989-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8703075&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Algebraic; Combinatorics; Association

This work is in the area of algebraic combinatorics. It includes association schemes ((P andQ)-polynomial association schemes and more general association schemes), distance-regular graphs, tight designs, perfect codes and spherical designs. Emphasis will be put on the interplay of algebraic combinatorics with the theory of orthogonal polynomials and with the representation theory of groups. It will start the general classification problem for general commutative association schemes of large class number. More precisely, it will collect many examples and calculate their character tables and find as many necessary conditions for the character table as needed for the classification. It will also study distance-regular graphs with fixed (small) valency and generalize such results to general commutative association schemes with small valency. It will also study extremal configurations of (finite) sets in association schemes and also in the sphere and other (nice) metric spaces. This research will concentrate on combinatorial aspect of algebraic problems. The combination of algebraic, number theoretic and analytic tools necessary to perform this research makes the subject very attractive. Bannai is one of the top leaders in this subject. Result of very great importance will surely result from this project.

这项工作属于代数组合学的范畴。它包括关联方案（(P和q)-多项式关联方案和更一般的关联方案）、距离正则图、紧密设计、完美码和球面设计。重点将放在代数组合学与正交多项式理论和群的表示理论的相互作用。它开启了大类数的一般交换关联方案的一般分类问题。更准确地说，它将收集许多示例并计算它们的字符表，并找到分类所需的尽可能多的字符表的必要条件。本文还将研究具有固定（小）价的距离正则图，并将这些结果推广到具有小价的一般交换关联方案。它还将研究关联方案中（有限）集的极值构型，以及球和其他（好的）度量空间中的极值构型。本研究将集中于代数问题的组合方面。进行这项研究所必需的代数、数论和分析工具的结合使这门学科非常有吸引力。班奈是这一领域的顶尖领导者之一。这个项目一定会产生非常重要的结果。