**Mathematical Surveys and Monographs**

Volume: 175;
2011;
298 pp;
Hardcover

MSC: Primary 05; 16; 20;
Secondary 15

Print ISBN: 978-0-8218-4496-0

Product Code: SURV/175

List Price: $99.00

AMS Member Price: $79.20

MAA member Price: $89.10

**Electronic ISBN: 978-1-4704-1402-3
Product Code: SURV/175.E**

List Price: $99.00

AMS Member Price: $79.20

MAA member Price: $89.10

#### Supplemental Materials

# Algebraic Design Theory

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*Warwick de Launey; Dane Flannery*

Combinatorial design theory is a source of simply stated, concrete, yet difficult discrete problems, with the Hadamard conjecture being a prime example. It has become clear that many of these problems are essentially algebraic in nature. This book provides a unified vision of the algebraic themes which have developed so far in design theory. These include the applications in design theory of matrix algebra, the automorphism group and its regular subgroups, the composition of smaller designs to make larger designs, and the connection between designs with regular group actions and solutions to group ring equations. Everything is explained at an elementary level in terms of orthogonality sets and pairwise combinatorial designs—new and simple combinatorial notions which cover many of the commonly studied designs. Particular attention is paid to how the main themes apply in the important new context of cocyclic development. Indeed, this book contains a comprehensive account of cocyclic Hadamard matrices. The book was written to inspire researchers, ranging from the expert to the beginning student, in algebra or design theory, to investigate the fundamental algebraic problems posed by combinatorial design theory.

#### Readership

Graduate students and research mathematicians interested in algebra or design theory.

#### Table of Contents

# Table of Contents

## Algebraic Design Theory

- Cover Cover11 free
- Title page i2 free
- Contents v6 free
- Preface ix10 free
- Announcement xi12 free
- Overview 114 free
- Many kinds of pairwise combinatorial designs 720
- A primer for algebraic design theory 2740
- Orthogonality 4962
- Modeling Λ-equivalence 6376
- The Grammian 7184
- Transposability 7790
- New designs from old 8598
- Automorphism groups 99112
- Group development and regular actions on arrays 119132
- Origins of cocyclic development 135148
- Group extensions and cocycles 145158
- Cocyclic pairwise combinatorial designs 161174
- Centrally regular actions 167180
- Cocyclic associates 177190
- Special classes of cocyclic designs 195208
- The Paley matrices 203216
- A large family of cocyclic Hadamard matrices 215228
- Substitution schemes for cocyclic Hadamard matrices 223236
- Calculating cocyclic development rules 239252
- Cocyclic Hadamard matrices indexed by elementary abelian groups 257270
- Cocyclic concordant systems of orthogonal designs 267280
- Asymptotic existence of cocyclic Hadamard matrices 279292
- Bibliography 287300
- Index 295308 free
- Back Cover Back Cover1314