Mathematical Sciences: Research in Algebraic Combinatorics

9311805瓦克斯该奖项支持瓦克斯教授致力于代数和计数组合学的研究。这一建议的第一部分也是主要部分涉及对偏序集拓扑性质的组合方面的研究。这些研究提供了组合学和其他数学分支，如拓扑学、代数和几何学之间的深层次和基本联系。这项研究属于组合学的一般领域。组合学试图找到有效的方法来研究如何组织离散的集合。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，如电话系统，以及计算机科学中的算法设计，都涉及离散对象，这利用了组合研究。***

9311805 Wachs This award supports the research of Professor Wachs to work in algebraic and enumerative combinatorics. The first and major part of this proposal deals with the study of combinatorial aspects of topological properties of partially ordered sets. These studies provide a deep and fundamental link between combinatorics and other branches of mathematics, such as topology, algebra and geometry. The research is in the general area of combinatorics. Combinatorics attempts to find efficient methods to study how discrete collections can be organized. The behavior of discrete systems is extremely important to modern communications. For example, the design of large networks, as in telephone systems, and the design of algorithms in computer science all deal with discrete objects, and this makes use of combinatorial research. ***