Mathematical Sciences: Embeddings, Latin Squares and Graph Decompositions

该奖项支持 C. Rodger 教授在组合学方面的研究。 他将致力于将 n 阶部分拉丁方嵌入到小于或等于 2n 阶拉丁方。 他还打算研究涉及嵌入三元组和图分解的问题。 该研究跨越了组合学和统计学领域。 组合学试图找到有效的方法来研究如何组织离散的对象集合。 因此，它对于现代通信极其重要，例如电话系统中的大型网络的设计。 本研究的主要对象是拉丁方，它是用于设计实验以及改善经济中许多生产领域的质量控制的基本工具。

This award supports the research of Professor C. Rodger to work in combinatorics. He will work on the embedding of partial latin squares of order n into latin squares of order less than or equal to 2n. He also intends to work on problems involving embedding triple systems and graph decompositions. The research crosses lines between the areas of combinatorics and statistics. Combinatorics attempts to find efficient methods to study how discrete collections of objects can be organized. And so it is extremely important to modern communications, for example the design of large networks as in telephone systems. The main object to be studied in the proposed research, latin squares, is a fundamental tool used in designing experiments and so in improving quality control in many areas of production within the economy.