Combinatorial Representation Theory: Constructive and Integral

利布勒这个奖项支持对各种详细研究方案的研究，包括循环和非交换差集、威廉姆森矩阵、特殊P-群的有限几何、割圆结合方案和积分Hecke代数。虽然每个主题本身都有很大的兴趣，但对这些主题的进一步研究也将有助于更广泛的目标，即发展一个可以建设性地使用的联合图式类结构的积分表示理论。这项调查是计算密集型的，严重依赖于高级计算机软件包。该奖项还支持在州际代数组合研讨会上的嘉宾演讲者。两周一次的研讨会使来自科罗拉多州和怀俄明州前线大学的学生和教职员工受益。这项研究属于组合学的一般领域。组合学的目标之一是找到有效的方法来研究离散的对象集合如何排列。离散系统的行为对于现代通信来说是极其重要的。例如，大型网络的设计，如那些发生在电话系统中的网络，以及计算机科学中的算法设计，都涉及离散的对象集，这利用了组合研究。这项研究的广泛目标是缩小某些类型的高度对称离散系统的已知例子与理论极限之间的差距。

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.