Combinatorics of Symmetric Designs

Erscheinungsjahr 2006
ISBN: 978-0-521-81833-9
Verlag: Cambridge University Press

Buch, Englisch, Band 5, 534 Seiten, Format (B × H): 161 mm x 235 mm, Gewicht: 975 g

Reihe: New Mathematical Monographs

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.

Autoren/Hrsg.

Ionin, Yury J

Shrikhande, Mohan S

Fachgebiete

• Interdisziplinäres Wissenschaften Wissenschaften: Forschung und Information Informationstheorie, Kodierungstheorie
• Mathematik | Informatik Mathematik Algebra Elementare Algebra
• Mathematik | Informatik EDV | Informatik Daten / Datenbanken Informationstheorie, Kodierungstheorie
• Mathematik | Informatik Mathematik Geometrie Algebraische Geometrie
• Mathematik | Informatik Mathematik Mathematik Allgemein Grundlagen der Mathematik

Inhaltsverzeichnis

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.

Über Autor(innen)

Shrikhande, Mohan S
Mohan S. Shrikhande is a Professor of Mathematics at Central.

Ionin, Yury J
Yury J. Ionin is a Professor of Mathematics at Central Michigan University, USA.