9400510 Stanton This award funds the work of Prof. Dennis Stanton in Combinatorics. Prof. Stanton will study the monotonicity of integer partitions. Classes of orthogonal polynomials will be studied as an aid to enumeration. Prof. Stanton will also investigate questions in representation theory, in particular the representations of the symmetric and general linear groups. The techniques used on these problems should be both combinatorial and analytic. This research falls in the broad category of combinatorics, which is one of the most active fields in today's mathematics. At its roots, combinatorics is the study of systematic counting. Counting can be incredibly difficult when the objects are difficult to list, and combinatorists look for general methods for overcoming these difficulties. Today's combinatorics makes use of a wide variety of the most advanced and modern mathematical techniques. Although its roots go back several centuries, the field has had an explosive development in the past few decades. This growth comes from its importance in communications and information technology and from the success of modern techniques to problems of counting.
