Description: Among the simplest combinatorial designs, triple systems are a natural generalization of graphs and have connections with geometry, algebra, group theory, finite fields, and cyclotomy. Applications of triple systems are found in coding theory, cryptography, computer science, and statistics. In many cases, triple systems provide the prototype for deep results in combinatorial design theory, and a number of important results were first understood in the context of triple systems and then generalized. This book attempts to survey current knowledge on the subject, to gather together common themes, and to provide an accurate portrait of the huge variety of problems and results. It includes representative samples of the major styles of proof technique and a comprehensive bibliography.
Review Quotes: "This magnificent bible on triple systems should belong on the shelves of everyone who works in triple systems and block designs. It will be a useful reference text for people in allied fields such as graph theory and cryptography. The level of the text is aimed at graduate and research use, although some chapters could be used as a basis for an honours student's project. . . . [J]ust about every other aspect of triple systems gets a mention somewhere in this great book, and the bibliography is sufficiently complete that it mentions related work not covered in the text." -- Mathematical Reviews