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Designs 2002

Further Computational and Constructive Design Theory

  • Book
  • © 2003

Overview

Editors:
  1. W. D. Wallis

    1. Southern Illinois University, USA

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

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Table of contents (13 chapters)

  1. Front Matter

    Pages i-xii
    Download chapter PDF

  2. The Existence of 2-SOLSSOMs

    • R. Julian, R. Abel, F. E. Bennett
    Pages 1-21

  3. Conjugate Orthogonal Diagonal Latin Squares with Missing Subsquares

    • Frank E. Bennett, Beiliang Du, Hantao Zhang
    Pages 23-45

  4. Combinatorial Trades: A Survey of Recent Results

    • Elizabeth J. Billington
    Pages 47-67

  5. Two-Stage Generalized Simulated Annealing for the Construction of Change-Over Designs

    • Yuk W. Cheng, Deborah J. Street, William H. Wilson
    Pages 69-79

  6. New Lower Bounds on the Maximum Number of Mutually Orthogonal Steiner Triple Systems

    • J. H. Dinitz, P. Dukes
    Pages 81-101

  7. On Minimal Defining Sets in AG(d,3)

    • Diane Donovan, Abdollah Khodkar, Anne Penfold Street
    Pages 103-131

  8. Hadamard Matrices, Orthogonal Designs and Construction Algorithms

    • Stelios Georgiou, Christos Koukouvinos, Jennifer Seberry
    Pages 133-205

  9. Constructing a Class of Designs with Proportional Balance

    • Ken Gray, Anne Penfold Street
    Pages 207-225

  10. Constructions Using Balanced n-ary Designs

    • Malcolm Greig
    Pages 227-254

  11. Sets of Steiner Triple Systems of Order 9 Revisited

    • T. S. Griggs, A. Rosa
    Pages 255-276

  12. Solving Isomorphism Problems for t-Designs

    • Reinhard Laue
    Pages 277-300

  13. Finding Double Youden Rectangles

    • N. C. K. Phillips, D. A. Preece
    Pages 301-315

  14. Kirkman Triple Systems and Their Generalizations: A Survey

    • Rolf S. Rees, W. D. Wallis
    Pages 317-368
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Keywords

About this book

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.

Editors and Affiliations

  • Southern Illinois University, USA

    W. D. Wallis

Bibliographic Information

  • Book Title: Designs 2002

  • Book Subtitle: Further Computational and Constructive Design Theory

  • Editors: W. D. Wallis

  • Series Title: Mathematics and Its Applications

  • DOI: https://doi.org/10.1007/978-1-4613-0245-2

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 2003

  • Hardcover ISBN: 978-1-4020-7599-5Published: 30 September 2003

  • Softcover ISBN: 978-1-4613-7958-4Published: 11 July 2012

  • eBook ISBN: 978-1-4613-0245-2Published: 01 December 2013

  • Edition Number: 2

  • Number of Pages: XII, 368

  • Topics: Combinatorics, Theory of Computation, Discrete Mathematics in Computer Science

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