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Algebraic Design Theory
 
Dane Flannery National University of Ireland, Galway, Ireland
Algebraic Design Theory
Hardcover ISBN:  978-0-8218-4496-0
Product Code:  SURV/175
List Price: $129.00
MAA Member Price: $116.10
AMS Member Price: $103.20
eBook ISBN:  978-1-4704-1402-3
Product Code:  SURV/175.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Hardcover ISBN:  978-0-8218-4496-0
eBook: ISBN:  978-1-4704-1402-3
Product Code:  SURV/175.B
List Price: $254.00 $191.50
MAA Member Price: $228.60 $172.35
AMS Member Price: $203.20 $153.20
Algebraic Design Theory
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Algebraic Design Theory
Dane Flannery National University of Ireland, Galway, Ireland
Hardcover ISBN:  978-0-8218-4496-0
Product Code:  SURV/175
List Price: $129.00
MAA Member Price: $116.10
AMS Member Price: $103.20
eBook ISBN:  978-1-4704-1402-3
Product Code:  SURV/175.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Hardcover ISBN:  978-0-8218-4496-0
eBook ISBN:  978-1-4704-1402-3
Product Code:  SURV/175.B
List Price: $254.00 $191.50
MAA Member Price: $228.60 $172.35
AMS Member Price: $203.20 $153.20
  • 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.

    Readership

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

  • Table of Contents
     
     
    • 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
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
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.

Readership

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
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.