Mathematical Sciences: Research in Algebraic Combinatorics

这个项目是关于代数组合学和由理论计算机科学驱动的组合学的研究。首席研究员将考虑与组合对象的部分有序集的代数和拓扑研究有关的问题，部分有序集的排序，以及与分布式计算相关的图着色。这项研究属于组合学的广泛范畴，这是当今数学中最活跃的领域之一。组合学代表了对所有数学活动——计数——的系统化。然而，在它的现代发展中，组合学已经超越了仅仅计算，它利用了各种各样的高级数学技术。由于其在通信和信息技术中的重要性，该领域在过去的几十年里有了爆炸性的发展。

This project is concerned with research in algebraic combinatorics and combinatorics motivated by theoretical computer science. The principal investigator will consider problems pertaining to an algebraic and topological investigation of partially ordered sets of combinatorial objects, sorting of partially ordered sets, and graph coloring in connection with distributed computing. This research falls in the broad category of combinatorics, which is one of the most active fields in today's mathematics. Combinatorics represents a systematization of the very first of all mathematical activities, counting. In its modern development, however, combinatorics has gone beyond just counting to make use of a wide variety of advanced mathematical techniques. The field has had an explosive development in the past few decades because of its importance in communications and information technology.