Ionin Y.J., Shrikhandale M.S. Combinatorics of Symmetric Designs

Cambridge University Press, 2006 — 534 pp. — (New Mathematical Monographs: 5).Providing a unified exposition of the theory of symmetric designs with emphasis on recent developments, this volume covers the combinatorial aspects of the theory, giving particular attention to the construction of symmetric designs and related objects. The last five chapters are devoted to balanced generalized weighing matrices, decomposable symmetric designs, subdesigns of symmetric designs, non-embeddable quasi-residual designs, and Ryser designs. The book concludes with a comprehensive bibliography of over 400 entries. Detailed proofs and a large number of exercises make it suitable as a text for an advanced course in combinatorial designs.The book contains many recent results and developments that have never appeared in book form, and an extensive bibliography contains more than 400 cited entries.
Self-contained and accessible to researchers and graduate students alike.
As there are a large number of exercises, and detailed proofs of important results, it can serve as a text for a graduate course in Combinatorial Designs.Combinatorics of finite sets.
Introduction to designs.
Vector spaces over finite fields.
Hadamard matrices.
Resolvable designs.
Symmetric designs and t-designs.
Symmetric designs and regular graphs.
Block intersection structure of designs.
Difference sets.
Balanced generalized weighing matrices.
Decomposable symmetric designs.
Subdesigns of symmetric designs.
Non-embeddable quasi-residual designs.
Ryser designs.
Appendix.