Mathematical Sciences: Embeddings, Latin Squares and Graph Decompositions

该奖项支持C.罗杰教授在组合学方面的研究。他将研究将n阶的拉丁偏方嵌入到小于等于2n阶的拉丁方中。他还打算研究涉及嵌入三重系统和图分解的问题。这项研究跨越了组合学和统计学的界限。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，它对现代通信非常重要，例如电话系统中大型网络的设计。本研究的主要研究对象是拉丁方尺，它是一种用于设计实验的基本工具，从而可以改善经济中许多生产领域的质量控制。

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.