Combinatorics of Symmetric Designs

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Overview

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.

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Editorial Reviews

From the Publisher
"I said that the book is more than a research monograph: in many places, it is fun to read! Unlike most research monographs, however, every chapter ends with exercises ranging from the routine to the very challenging, and every chapter ends with notes on sources, history, and references to the chapter's topics. The exercises and notes are among the most attractive aspect of the book."
Ezra Brown MAA Reviews

"The strengths of this book are the many combinatorial connections, the comprehensive and carefully described constructions, and the extensive list of references."
Sylvia A. Hobart, Mathematical Reviews

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Product Details

  • ISBN-13: 9780521818339
  • Publisher: Cambridge University Press
  • Publication date: 4/30/2006
  • Series: New Mathematical Monographs Series , #5
  • Edition description: New Edition
  • Pages: 534
  • Product dimensions: 5.98 (w) x 8.98 (h) x 1.18 (d)

Meet the Author

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

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

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Table of 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.

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