An algebraic approach to the Erdos-Ko-Rado theorem

Erdos-Ko-Rado 定理的代数方法

• 批准号: 341214-2013
• 负责人: Meagher, Karen
• 金额: $ 1.09万
• 依托单位: University of Regina
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2016
• 资助国家: 加拿大
• 起止时间: 2016-01-01 至 2017-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=595349
• 关键词: algebraic; approach; Erdos; Ko; Rado

Design theory and extremal set theory are the study of systems of sets (and other combinatorial objects) that satisfy some collection of properties (perhaps the sets must intersect in specific patterns or maybe the sets cannot be subsets of one another). This field of research typically includes finding constructions for specific types of systems and the determination of the size and structure of the maximum systems with a specific restriction. This is an important research area since these designs are often used in applications. For example, one design I study are covering arrays which are used to design effective test suites for software and networks.

设计理论和极值集合论是研究满足某些性质集合的集合系统（和其他组合对象）（也许集合必须以特定模式相交，或者集合不能是彼此的子集）。该研究领域通常包括为特定类型的系统寻找结构，以及确定具有特定限制的最大系统的大小和结构。这是一个重要的研究领域，因为这些设计经常用于应用程序。例如，我研究的一个设计是覆盖阵列，用于为软件和网络设计有效的测试套件。