Mathematical Sciences: Universal Cycles and Partially Ordered Sets

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This award supports the research of Professor Glen Hurlbert for research in graph theory and other areas of combinatorics. Professor Hurlbert will study universal cycles and partially ordered sets as well as problems in combinatorial number theory and combinatorial geometry. Graph Theory go back perhaps two hundred years, but only in the last half-century has the field become an active, fertile, and flourishing branch of mathematics. A graph is a network of lines ("edges") joining points ("vertices"), thus the language of graphs becomes a natural way of describing interrelationships among separated objects. Graph Theory figures most prominently as an essential tool in Communications Theory and Computer Science. Combinatorics attempts to find efficient methods to study how discrete collections of objects can be organized. And, so it to is extremely important to modern communications.