ABSTRACT
In broad terms, the study of combinatorial designs is the study of the structure of collections of subsets of a finite set when these collections of subsets satisfy certain prescribed properties. In particular, a block design has the property that every one of these subsets has the same size k and every pair of points in the set is in exactly the same number of these subsets. Latin squares are also fundamental in this area and can be thought of in this context, but they are commonly thought of as n × n arrays with the property that each cell contains one element from an n-set and each row and each column contain each element exactly once. Some of the questions of general interest include: existence of designs, enumeration of nonisomorphic designs, and the study of subdesigns of designs.
