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Algebraic Design Theory

Dane Flannery National University of Ireland, Galway, Ireland
Available Formats:
Hardcover ISBN: 978-0-8218-4496-0
Product Code: SURV/175
List Price: $105.00 MAA Member Price:$94.50
AMS Member Price: $84.00 Electronic ISBN: 978-1-4704-1402-3 Product Code: SURV/175.E List Price:$99.00
MAA Member Price: $89.10 AMS Member Price:$79.20
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List Price: $157.50 MAA Member Price:$141.75
AMS Member Price: $126.00 Click above image for expanded view Algebraic Design Theory Dane Flannery National University of Ireland, Galway, Ireland Available Formats:  Hardcover ISBN: 978-0-8218-4496-0 Product Code: SURV/175  List Price:$105.00 MAA Member Price: $94.50 AMS Member Price:$84.00
 Electronic ISBN: 978-1-4704-1402-3 Product Code: SURV/175.E
 List Price: $99.00 MAA Member Price:$89.10 AMS Member Price: $79.20 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$157.50 MAA Member Price: $141.75 AMS Member Price:$126.00
• Book Details

Mathematical Surveys and Monographs
Volume: 1752011; 298 pp
MSC: Primary 05; 16; 20; Secondary 15;

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.

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

• Chapters
• 1. Overview
• 2. Many kinds of pairwise combinatorial designs
• 3. A primer for algebraic design theory
• 4. Orthogonality
• 5. Modeling $\Lambda$-equivalence
• 6. The Grammian
• 7. Transposability
• 8. New designs from old
• 9. Automorphism groups
• 10. Group development and regular actions on arrays
• 11. Origins of cocyclic development
• 12. Group extensions and cocycles
• 13. Cocyclic pairwise combinatorial designs
• 14. Centrally regular actions
• 15. Cocyclic associates
• 16. Special classes of cocyclic designs
• 17. The Paley matrices
• 18. A large family of cocyclic Hadamard matrices
• 19. Substitution schemes for cocyclic Hadamard matrices
• 20. Calculating cocyclic development rules
• 21. Cocyclic Hadamard matrices indexed by elementary abelian groups
• 22. Cocyclic concordant systems of orthogonal designs
• 23. Asymptotic existence of cocyclic Hadamard matrices

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Volume: 1752011; 298 pp
MSC: Primary 05; 16; 20; Secondary 15;

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.

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

• Chapters
• 1. Overview
• 2. Many kinds of pairwise combinatorial designs
• 3. A primer for algebraic design theory
• 4. Orthogonality
• 5. Modeling $\Lambda$-equivalence
• 6. The Grammian
• 7. Transposability
• 8. New designs from old
• 9. Automorphism groups
• 10. Group development and regular actions on arrays
• 11. Origins of cocyclic development
• 12. Group extensions and cocycles
• 13. Cocyclic pairwise combinatorial designs
• 14. Centrally regular actions
• 15. Cocyclic associates
• 16. Special classes of cocyclic designs
• 17. The Paley matrices
• 18. A large family of cocyclic Hadamard matrices
• 19. Substitution schemes for cocyclic Hadamard matrices
• 20. Calculating cocyclic development rules
• 21. Cocyclic Hadamard matrices indexed by elementary abelian groups
• 22. Cocyclic concordant systems of orthogonal designs
• 23. Asymptotic existence of cocyclic Hadamard matrices
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