Mathematical Sciences: Formal Systems and Combinatorics

数学科学：形式系统和组合学

• 批准号: 8617399
• 负责人: Timothy Carlson
• 金额: --
• 依托单位: Ohio State University Research Foundation -DO NOT USE
• 依托单位国家: 美国
• 项目类别: Continuing grant
• 财政年份: 1987
• 资助国家: 美国
• 起止时间: 1987-05-01 至 1991-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8617399&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Formal; Systems; Combinatorics

Timothy Carlson's work in finite and infinite combinatorics provides powerful unifying generalizations of various so-called Ramsey theorems. The simplest Ramsey theorem is the following: if six points in space are connected in all possible ways by straight line segments and each segment is painted either red or green, then there will always be an entire triangle whose sides are of the same color. This theorem has been generalized beyond easy recognition in a variety of different ways, but all such generalizations are referred to as Ramsey theorems. They have a host of significant consequences in geometry and number theory and elsewhere, and it is very useful to have unifying principles which provide economical derivations for these corollaries. Further results of this nature will be sought.

Timothy Carlson在有限和无限组合学方面的工作 提供了强大的统一概括各种所谓的 Ramsey定理 最简单的Ramsey定理如下： 如果空间中的六个点以所有可能的方式连接， 直线段，每段都涂成红色或 绿色，那么总有一个三角形， 是同一种颜色。 这个定理已经被推广到 以各种不同的方式容易识别，但所有这些 一般化被称为拉姆齐定理。 他们有一个 几何学和数论中的一系列重要结果 和其他地方，有统一的原则是非常有用的， 这为这些推论提供了经济的推导。 将寻求这类性质的进一步结果。