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Designs 2002

Further Computational and Constructive Design Theory

  • W. D. Wallis

Part of the Mathematics and Its Applications book series (MAIA, volume 563)

Table of contents

  1. Front Matter
    Pages i-xii
  2. R. Julian, R. Abel, F. E. Bennett
    Pages 1-21
  3. Frank E. Bennett, Beiliang Du, Hantao Zhang
    Pages 23-45
  4. Elizabeth J. Billington
    Pages 47-67
  5. Yuk W. Cheng, Deborah J. Street, William H. Wilson
    Pages 69-79
  6. Diane Donovan, Abdollah Khodkar, Anne Penfold Street
    Pages 103-131
  7. Stelios Georgiou, Christos Koukouvinos, Jennifer Seberry
    Pages 133-205
  8. Ken Gray, Anne Penfold Street
    Pages 207-225
  9. Malcolm Greig
    Pages 227-254
  10. T. S. Griggs, A. Rosa
    Pages 255-276
  11. Reinhard Laue
    Pages 277-300
  12. N. C. K. Phillips, D. A. Preece
    Pages 301-315
  13. Rolf S. Rees, W. D. Wallis
    Pages 317-368

About this book

Introduction

This volume is a sequel to our 1996 compilation, Computational and Constructive Design Theory. Again we concentrate on two closely re­ lated aspects of the study of combinatorial designs: design construction and computer-aided study of designs. There are at least three classes of constructive problems in design theory. The first type of problem is the construction of a specific design. This might arise because that one particular case is an exception to a general rule, the last remaining case of a problem, or the smallest unknown case. A good example is the proof that there is no projective plane of parameter 10. In that case the computations involved were not different in kind from those which have been done by human brains without electronic assistance; they were merely longer. Computers have also been useful in the study of combinatorial spec­ trum problems: if a class of design has certain parameters, what is the set of values that the parameters can realize? In many cases, there is a recursive construction, so that the existence of a small number of "starter" designs leads to the construction of infinite classes of designs, and computers have proven very useful in finding "starter" designs.

Keywords

algorithms computer construction latin square Notation sets

Editors and affiliations

  • W. D. Wallis
    • 1
  1. 1.Southern Illinois UniversityUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4613-0245-2
  • Copyright Information Springer Science+Business Media New York 2003
  • Publisher Name Springer, Boston, MA
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4613-7958-4
  • Online ISBN 978-1-4613-0245-2
  • Buy this book on publisher's site