Computational and Constructive Design Theory

  • W. D. Wallis

Table of contents

  1. Front Matter
    Pages i-xiv
  2. W. D. Wallis
    Pages 1-12
  3. Steven Furino
    Pages 13-28
  4. Rudolf Mathon
    Pages 29-48
  5. Daniel Ashlock
    Pages 49-65
  6. Charles J. Colbourn, Jeffrey H. Dinitz
    Pages 67-134
  7. William Kocay
    Pages 135-175
  8. Brendan D. McKay, Stanisław P. Radziszowski
    Pages 177-188
  9. W. H. Mills
    Pages 189-226
  10. Lucia Moura
    Pages 227-254
  11. Martin J. Sharry, Anne Penfold Street
    Pages 255-335
  12. G. H. J. van Rees
    Pages 337-357
  13. Back Matter
    Pages 359-362

About this book

Introduction

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.

Keywords

Morphism Volume algorithms bridge computation computer construction design eXist genetic algorithm genetic algorithms

Editors and affiliations

  • W. D. Wallis
    • 1
  1. 1.Department of MathematicsSouthern Illinois UniversityCarbondaleUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4757-2497-4
  • Copyright Information Springer-Verlag US 1996
  • Publisher Name Springer, Boston, MA
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4757-2499-8
  • Online ISBN 978-1-4757-2497-4
  • About this book