Mathematical Sciences: Partially Ordered Sets

数学科学：偏序集

• 批准号: 8902481
• 负责人: William Trotter
• 金额: $ 18.8万
• 依托单位: Arizona State University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1989
• 资助国家: 美国
• 起止时间: 1989-06-15 至 1992-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8902481&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Partially; Ordered; Sets

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.

该奖项支持组合数学的研究， William T.亚利桑那州立大学的特罗特。博士 Trotter的研究计划是研究偏序集， 图和其他离散结构，特别强调 关于组合算法和极值问题。中 他将研究的中心问题是： 在亏格n的表面上绘制的地图的面网格;在线 着色、分区和其他优化算法 问题;和偏序集的极值问题。 这项研究福尔斯属于组合学的大范畴， 这是当今数学中最活跃的领域之一。 从根本上说，组合数学代表了一个系统化的 首先是数学活动，计数在其 然而，现代的发展，组合数学已经不仅仅是 计数利用各种先进的数学 技术，虽然它的根源可以追溯到几个世纪， 在过去的几十年里， 因为它在通信和信息方面的重要性， 技术.