Combinatorial Design Theory - Notes

Combinatorial design theory traces its origins to statistical theory of experimental design but also to recreational mathematics of the 19th century and to geometry. In the past forty years combinatorial design theory has developed into a vibrant branch of combinatorics with its own aims, methods and problems. It has found substantial applications in other branches of combinatorics, in graph theory, coding theory, theoetical computer science, statistics, and algebra, among others. The main problems in design theory are, generally speaking, those of the existence, enumeration and classification, structural properties, and applications. It is not the objective of these notes to give a comprehensive abbreviated overview of combinatorial design theory but rather to provide an introduction to developing a solid basic knowledge of problems and methods of combinatorial design theory, with an indication of its flavour and breadth, up to a level that will enable one to approach open research problems. Towards this objective, most of the needed definitions are provided.