Mathematical Sciences: Partially Ordered Sets

该奖项支持亚利桑那州立大学威廉·T·特罗特教授在组合学方面的研究。特罗特博士的研究计划是研究偏序集、图和其他离散结构，重点是组合算法和极值问题。他将研究的中心问题包括：在亏格n的曲面上绘制的映射的面格的阶数维；着色、划分和其他优化问题的在线算法；以及偏序集的极值问题。这项研究属于组合学的广泛范畴，它是当今数学中最活跃的领域之一。从根本上说，组合学代表着对所有数学活动中的第一个--计数--的系统化。然而，在它的现代发展中，组合数学已经不仅仅是利用各种先进的数学技术，尽管它的根源可以追溯到几个世纪前，但由于它在通信和信息技术中的重要性，该领域在过去几十年里有了爆炸性的发展。

This award supports the research in Combinatorics of Professor William T. Trotter of Arizona State University. Dr. Trotter's research plan is to study partially ordered sets, graphs, and other discrete structures, with particular emphasis on combinatorial algorithms and extremal problems. Among the central problems he will investigate are: the order dimension of the face lattice of a map drawn on a surface of genus n; online algorithms for coloring, partitioning, and other optimization problems; and extremal problems for partially ordered sets. This research falls in the broad category of Combinatorics, which is one of the most active fields in today's mathematics. Fundamentally, 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, and although its roots go back several centuries, the field has had an explosive development in the past few decades because of its importance in communications and information technology.