Mathematical Sciences: Block Designs and Related Combinatorial Structures

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。林德纳博士的研究重点将集中在偏图分解的小嵌入问题，完全图的2-完全分解成环的存在性问题，以及正交和垂直阵列的共轭不变子群问题。这项研究属于组合学的广泛范畴，这是当今数学中最活跃的领域之一。从根本上说，组合学代表了对所有数学活动——计数——的系统化。然而，在其现代发展中，组合学已经不仅仅是计算，而是利用了各种各样的先进数学技术。尽管它的根源可以追溯到几个世纪以前，但由于它在通信和信息技术中的重要性，该领域在过去的几十年里有了爆炸性的发展。

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.