Combinatorial matrix theory

拟议的研究探讨了两个不同的数学领域，即图论和代数之间的相互作用。作为一个生物学家可能会研究一个有机体和有机体的组成部分的相互关系，我的研究探索图形和矩阵的组成部分之间的联系。正在探索的一个特殊类型的问题是如何数学数组是影响定性信息，由积极的模式，消极的和零的项目在数组中。有时，仅此信息就可以独立于数组中各个数字的大小来限制结果。典型的纯数学，这项研究并不专注于任何特定的应用，只是探索理论及其抽象对象的复杂性。然而，一些涉及的数学问题确实出现在电信、统计设计理论和动力系统中。

The proposed research explores the interplay between two different areas of mathematics, namely graph theory and algebra. As a biologist might study an organism and the interelationship of component parts of the ogranism, my research explores connections between the components of graphs and matrices. One particular type of problem being explored is how mathematics on arrays of numbers is affected by qualitative information, by the pattern of postive, negative and zero entries in the array. Sometimes this information alone restricts results independently of the magnitude of the individual numbers in the array. Typical of pure mathematics, this research is not focusing on any particular application, merely exploring the intricacies of the theory and its abstract objects. Some of the mathematics involved however did arise out of problems in telecommunications, statstical desgin theory and dynamical systems.