Combinatorics of Symmetric Designs

A unified and comprehensive exposition of the theory of symmetric designs with emphasis on recent developments.

Yury J. Ionin (Author), Mohan S. Shrikhande (Author)

9780521818339, Cambridge University Press

Hardback, published 25 May 2006

534 pages, 200 exercises
23.5 x 15.9 x 3 cm, 0.982 kg

'Most results in these chapters have never appeared in book form. Researchers in all areas of combinational designs, including coding theory and finite geometries, will find much of interest here. Detailed proofs and a large number of exercises make this book suitable as a text for an advance course in combinatorial designs.' L'enseignement mathematique

The aim of this book is to provide a unified exposition of the theory of symmetric designs with emphasis on recent developments. The authors cover the combinatorial aspects of the theory giving particular attention to the construction of symmetric designs and related objects. The last five chapters of the book are devoted to balanced generalized weighing matrices, decomposable symmetric designs, subdesigns of symmetric designs, non-embeddable quasi-residual designs, and Ryser designs. Most results in these chapters have never previously appeared in book form. The book concludes with a comprehensive bibliography of over 400 entries. Researchers in all areas of combinatorial designs, including coding theory and finite geometries, will find much of interest here. Detailed proofs and a large number of exercises make this book suitable as a text for an advanced course in combinatorial designs.

1. Combinatorics of finite sets
2. Introduction to designs
3. Vector spaces over finite fields
4. Hadamard matrices
5. Resolvable designs
6. Symmetric designs and t-designs
7. Symmetric designs and regular graphs
8. Block intersection structure of designs
9. Difference sets
10. Balanced generalized weighing matrices
11. Decomposable symmetric designs
12. Subdesigns of symmetric designs
13. Non-embeddable quasi-residual designs
14. Ryser designs
Appendix
Bibliography
Index.

Subject Areas: Communications engineering / telecommunications [TJK], Combinatorics & graph theory [PBV], Information theory [GPF]