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Association Schemes
Designed Experiments, Algebra and Combinatorics

$60.99 (P)

Part of Cambridge Studies in Advanced Mathematics

  • Date Published: March 2011
  • availability: Available
  • format: Paperback
  • isbn: 9780521188012

$ 60.99 (P)
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About the Authors
  • R.A. Bailey covers in this study the mathematics of association schemes--an area lying between pure mathematics and statistics that relates to the optimal design of scientific experiments. The book is accessible to mathematicians as well as statisticians. Arising from a graduate course taught by the author, it appeals to students as well as researchers as a valuable reference work from which to learn about the statistical/combinatorial aspects of their work.

    • Written to be accessible to both pure mathematicians and statisticians
    • Based on a graduate course on association schemes and the optimal design of scientific experiments
    • Minimum prerequisites and numerous examples and exercises make book also suitable for self-study
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    Reviews & endorsements

    "The author of this impressive monograph is well-known as a world leader who has made fundamental contributions to this field. Now she has come up with this elegantly written volume that provides a unified survey of the developments in and around association schemes...While the presentation has throughout been lucid and well-organized, the book maintains a high level of mathematical rigour and depth. The impressive list of references, including the most up-to-date ones, will make the book particularly valuable. The large number of examples and exercises, all meticulously chosen, will certainly endear the book to its readers. The author has done a tremendous job, and the scientific community will be the beneficiary. This marvelous book should find a place on the bookshelf of any serious researcher in experimental design and combinatorial theory."
    Sankhya: The Indian Journal of Statistics

    "Bailey makes the connections and justifies this book's place in the library. Highly recommended."
    D.V. Feldman, University of New Hampshire, CHOICE

    "Rosemary Bailey's book is a valuable contribution to one of the important aspects of commutative scheme theory: the application of commutative scheme theory to statistics. Scheme theorists will be grateful for this contribution, because it fills one of the many gaps in the global view of schemes and their central role in mathematics."
    Bulletin of the AMS

    "Those interested in experimental design will see this book in the finest tradition of mathematical statistics. It is thorough, precise, and comprehensive within its reach."
    Journal of the American Statistical Association

    "I think the author deserves applause for this book from everybody who is interested in schemes."
    Mathematics Reviews

    "This book will be a welcome addition to researchers in the area of association schemes as it is comprehensive and indicates likely directions for future work."
    Journal of the Royal Statistical Society

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    Product details

    • Date Published: March 2011
    • format: Paperback
    • isbn: 9780521188012
    • length: 406 pages
    • dimensions: 229 x 152 x 21 mm
    • weight: 0.54kg
    • availability: Available
  • Table of Contents

    1. Association schemes
    2. The Bose–Mesner algebra
    3. Combining association schemes
    4. Incomplete-block designs
    5. Partial balance
    6. Families of partitions
    7. Designs for structured sets
    8. Groups
    9. Posets
    10. Subschemes, quotients, duals and products
    11. Association schemes on the same set
    12. Where next?
    13. History and references.

  • Author

    R. A. Bailey, Queen Mary University of London

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