Description

This is the first volume of the second edition of the standard text on design theory. This is the first volume of the second edition of the standard text on design theory. It is suitable for advanced courses and as a reference work, not only for researchers in discrete mathematics or finite algebra, but also for those working in computer and communications engineering and other mathematically oriented disciplines. This is the first volume of the second edition of the standard text on design theory. It is suitable for advanced courses and as a reference work, not only for researchers in discrete mathematics or finite algebra, but also for those working in computer and communications engineering and other mathematically oriented disciplines. This is the first volume of the second edition of the standard text on design theory. Since the first edition there has been extensive development of the theory and this book has been thoroughly rewritten and extended during that time. In particular the growing importance of discrete mathematics to many parts of engineering and science have made designs a useful tool for applications. It is suitable for advanced courses and as a reference work, not only for researchers in discrete mathematics or finite algebra, but also for those working in computer and communications engineering and other mathematically oriented disciplines. Exercises are included throughout, and the book concludes with an extensive and updated bibliography of well over 1800 items. 1. Examples and basic definitions; 2. Combinatorial analysis of designs; 3. Groups and designs; 4. Witt designs and Mathieu groups; 5. Highly transitive groups; 6. Difference sets and regular symmetric designs; 7. Difference families; 8. Further direct constructions.