This award supports the research in Combinatorics of Professor William T. Trotter of Arizona State University. Dr. Trotter's research plan is to study partially ordered sets, graphs, and other discrete structures, with particular emphasis on combinatorial algorithms and extremal problems. Among the central problems he will investigate are: the order dimension of the face lattice of a map drawn on a surface of genus n; online algorithms for coloring, partitioning, and other optimization problems; and extremal problems for partially ordered sets. 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.
