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Computational and Constructive Design Theory

  • Book
  • © 1996

Overview

Editors:
  1. W. D. Wallis

    1. Department of Mathematics, Southern Illinois University, Carbondale, USA

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Table of contents (11 chapters)

  1. Front Matter

    Pages i-xiv
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  2. A Bridge Club Design

    • W. D. Wallis
    Pages 1-12

  3. The First Time

    • Steven Furino
    Pages 13-28

  4. Computational Methods in Design Theory

    • Rudolf Mathon
    Pages 29-48

  5. Finding Designs with Genetic Algorithms

    • Daniel Ashlock
    Pages 49-65

  6. Making the Mols Table

    • Charles J. Colbourn, Jeffrey H. Dinitz
    Pages 67-134

  7. On Writing Isomorphism Programs

    • William Kocay
    Pages 135-175

  8. The Nonexistence of 4-(12,6,6) Designs

    • Brendan D. McKay, StanisÅ‚aw P. Radziszowski
    Pages 177-188

  9. BIBDs with κ = 6 and λ = 1

    • W. H. Mills
    Pages 189-226

  10. Polyhedral Methods in Design Theory

    • Lucia Moura
    Pages 227-254

  11. Another Look at Large Sets of Steiner Triple Systems

    • Martin J. Sharry, Anne Penfold Street
    Pages 255-335

  12. (22, 33, 12, 8, 4)-BIBD, an Update

    • G. H. J. van Rees
    Pages 337-357

  13. Back Matter

    Pages 359-362
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Keywords

About this book

Over the last several years, there has been a significant increase in compu­ tational combinatorics. The most widely reported results were, of course, the proof of the Four Color Theorem and the proof that there is no projective plane of parameter 10. Although the computer was essential in both proofs, the only reason for this was the fact that life is short. The computations involved were not different in kind from those which have been done by human brains without electronic assistance; they were just longer. Another important fact to notice is that both problems were theoretical, pure­ mathematical ones. The pursuit of the Four-Color Theorem has led to the development of whole branches of graph theory. The plane of parameter 10 is not an isolated case; its nonexistence is the first (and so far, the only) coun­ terexample to the conjecture that the Bruck-Chowla-Ryser conditions were necessary and sufficient for the existence of a symmetric balanced incomplete block design; the study of this problem has also led to a number of theoretical advances, including investigation of the relationship between codes and designs.

Editors and Affiliations

  • Department of Mathematics, Southern Illinois University, Carbondale, USA

    W. D. Wallis

Bibliographic Information

  • Book Title: Computational and Constructive Design Theory

  • Editors: W. D. Wallis

  • DOI: https://doi.org/10.1007/978-1-4757-2497-4

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media Dordrecht 1996

  • eBook ISBN: 978-1-4757-2497-4Published: 29 June 2013

  • Edition Number: 1

  • Number of Pages: XIV, 362

  • Number of Illustrations: 5 b/w illustrations

  • Topics: Combinatorics, Algorithms, Discrete Mathematics in Computer Science

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