Structure in designs, coverings and decompositions

设计、覆盖和分解的结构

• 批准号: 170220-2011
• 负责人: Danziger, Peter
• 金额: $ 0.73万
• 依托单位: Ryerson University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2012
• 资助国家: 加拿大
• 起止时间: 2012-01-01 至 2013-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=508404
• 关键词: Structure; designs; coverings; decompositions

Combinatorial Designs provide an ideal way to understand the interaction properties of complex discrete structures, such as networks; a way to investigate the `interconnectedness' properties of such structures. The central focus of the proposed research program is the investigation of the structure of combinatorial designs; to consider designs with a particular structure, or lack thereof. Development in this area will provide a deeper understanding of the structure of the objects involved as well as insight into other combinatorial questions. Designs have well-known applications to statistics, coding theory and scheduling, in addition, there are potential applications to such diverse questions as algorithmic efficiency, software and network testing and numerical analysis. I have long been involved with finding various kinds of factorizations, initially uniform and class-uniformly resolvable designs, broadening this work to include more general factorizations, most notably cycle factorizations. I have also considered cases where factorization is not possible. More recently, I have become interested in Covering Arrays. This project will support my work in all of these areas.

组合设计为理解复杂离散结构(如网络)的相互作用属性提供了一种理想的方法，也是研究这种结构的“互连性”属性的一种方法。拟议的研究计划的中心焦点是调查组合设计的结构；考虑具有特定结构的设计，或不具有特定结构的设计。这一领域的发展将提供对所涉及对象的结构的更深入的理解，以及对其他组合问题的洞察。设计在统计学、编码理论和调度方面有着广泛的应用，此外，在算法效率、软件和网络测试以及数值分析等问题上也有潜在的应用。我长期以来一直致力于寻找各种分解，初始一致和类一致可分解的设计，将这项工作扩大到包括更一般的分解，最著名的是循环分解。我还考虑过不可能进行因式分解的情况。最近，我开始对介绍数组感兴趣。这个项目将支持我在所有这些领域的工作。