Combinatorics of Symmetric Designs

Yury J. Ionin; Mohan S. Shrikhande

doi:10.1017/CBO9780511542992

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Yury J. Ionin, Central Michigan University, Mohan S. Shrikhande, Central Michigan University

Publisher:: Cambridge University Press
Online publication date:: February 2010
Print publication year:: 2006
Online ISBN:: 9780511542992
DOI:: https://doi.org/10.1017/CBO9780511542992

Subjects:: Mathematics (general), Mathematics, Discrete Mathematics Information Theory and Coding
Series:: New Mathematical Monographs (5)

180.00 (USD)

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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.

'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.'

Source: L'enseignement mathematique

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Combinatorics of Symmetric Designs

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Contents

Frontmatter
pp i-vi

Contents
pp vii-x

Preface
pp xi-xiv

1 - Combinatorics of finite sets
pp 1-13

2 - Introduction to designs
pp 14-58

3 - Vector spaces over finite fields
pp 59-112

4 - Hadamard matrices
pp 113-153

5 - Resolvable designs
pp 154-185

6 - Symmetric designs and t-designs
pp 186-211

7 - Symmetric designs and regular graphs
pp 212-246

8 - Block intersection structure of designs
pp 247-288

9 - Difference sets
pp 289-322

10 - Balanced generalized weighing matrices
pp 323-367

11 - Decomposable symmetric designs
pp 368-406

12 - Subdesigns of symmetric designs
pp 407-428

13 - Non-embeddable quasi-residual designs
pp 429-446

14 - Ryser designs
pp 447-487

Appendix
pp 488-494

References
pp 495-513

Index
pp 514-519

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Combinatorics of Symmetric Designs

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