対称デザインの組合せ論 Combinatorics of Symmetric Designs (New Mathematical Monographs)

Ionin, Yury J./ Shrikhande, Mohan S.

Cambridge University Press（2006/05発売）

• 製本 Hardcover:ハードカバー版／ページ数 534 p.／サイズ 200 exercises, 170 worked examples
• 言語 ENG
• 商品コード 9780521818339
• DDC分類 511.6

Full Description

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.

Contents

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.