Mathematical Sciences: Block Designs and Related Combinatorial Structures

数学科学：块设计和相关组合结构

• 批准号: 8913576
• 负责人: Charles Lindner
• 金额: $ 2.63万
• 依托单位: Auburn University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1989
• 资助国家: 美国
• 起止时间: 1989-11-01 至 1993-10-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8913576&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Block; Designs; Related

This award supports the research in combinatorial design theory and graph theory of Professor Charles Lindner of Auburn University. The emphasis of Dr. Lindner's research will be on problems in small embeddings of partial graph decompositions, the existence problem of 2-perfect decompositions of the complete graph into cycles, and the conjugate invariant subgroup problem for both orthogonal and perpendicular arrays. 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.

该奖项支持奥本大学 Charles Lindner 教授在组合设计理论和图论方面的研究。 Lindner 博士的研究重点是部分图分解的小嵌入问题、完整图的 2-完美分解成循环的存在问题以及正交和垂直数组的共轭不变子群问题。 这项研究属于组合数学的广泛范畴，组合数学是当今数学中最活跃的领域之一。 从根本上说，组合学代表了所有数学活动中最重要的活动——计数的系统化。然而，在其现代发展中，组合数学已经超越了单纯的计数，而是利用了各种先进的数学技术，尽管其根源可以追溯到几个世纪前，但由于其在通信和信息技术中的重要性，该领域在过去几十年中取得了爆炸性的发展。