Combinatorial Representation Theory: Constructive and Integral

组合表示理论：构造性和积分

• 批准号: 9622458
• 负责人: Robert Liebler
• 金额: $ 6万
• 依托单位: Colorado State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1996
• 资助国家: 美国
• 起止时间: 1996-07-01 至 2000-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9622458&HistoricalAwards=false
• 关键词: Combinatorial; Representation; Theory; Constructive; Integral

Liebler This award supports an investigation into a variety of detailed research programs, including cyclic and non-abelian difference sets, Williamson matrices, finite geometries from special p-groups, cyclotomic association schemes and integral Hecke algebras. Although each is of substantial interest in its own right, further study of each of these topics will also contribute to the broader goal of development of an integral representation theory for association scheme-like structures that can be used constructively. This investigation is computation-intensive, relying heavily on the high-level computer software packages. This award also supports guest speakers at an interstate Algebraic Combinatorics Seminar. The biweekly seminar benefits students and faculty from universities along the front range of Colorado and Wyoming. This research is in the general area of Combinatorics. One of the goals of Combinatorics is to find efficient methods of studying 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. The broad goal of this research is to narrow the gap between the known examples and theoretical limits on certain types of highly symmetric discrete systems.

利布莱尔 该奖项支持对各种详细的研究计划进行调查，包括循环和非阿贝尔差集，威廉姆森矩阵，特殊p群的有限几何，分圆关联计划和积分Hecke代数。虽然每一个都是实质性的利益，在其本身的权利，进一步研究这些主题中的每一个也将有助于更广泛的目标，发展一个完整的表示理论的关联图式结构，可以建设性地使用。这项调查是计算密集型的，严重依赖于高级计算机软件包。该奖项还支持州际代数组合学研讨会的客座演讲者。每两周一次的研讨会使科罗拉多和怀俄明州前线沿着大学的学生和教师受益。 这项研究是在组合数学的一般领域。组合数学的目标之一是找到有效的方法来研究如何安排对象的离散集合。 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，如电话系统中出现的网络，以及 计算机科学中的算法处理对象的离散集合，这就利用了组合研究。广大 这项研究的目的是缩小已知的 某些类型的高度 对称离散系统