Mathematical Sciences: Research in Algebraic Combinatorics

小行星9311805 该奖项支持瓦克斯教授在代数和枚举组合学方面的研究。 这个建议的第一个和主要部分涉及研究偏序集的拓扑性质的组合方面。 这些研究提供了组合数学和其他数学分支，如拓扑学，代数和几何之间的深刻和根本的联系。 该研究是在组合学的一般领域。 组合数学试图找到有效的方法来研究如何组织离散的集合。 离散系统的行为对现代通信极为重要。 例如，大型网络的设计，如电话系统，以及计算机科学中算法的设计都涉及离散对象，这就需要使用组合研究。 ***

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. ***