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Parallelisms of Complete Designs


Part of London Mathematical Society Lecture Note Series

  • Date Published: June 1976
  • availability: Available
  • format: Paperback
  • isbn: 9780521211604

£ 28.99

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About the Authors
  • These notes present an investigation of a condition similar to Euclid's parallel axiom for subsets of finite sets. The background material to the theory of parallelisms is introduced and the author then describes the links this theory has with other topics from the whole range of combinatorial theory and permutation groups. These include network flows, perfect codes, Latin squares, block designs and multiply-transitive permutation groups, and long and detailed appendices are provided to serve as introductions to these various subjects. Many of the results are published for the first time.

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    Product details

    • Date Published: June 1976
    • format: Paperback
    • isbn: 9780521211604
    • length: 152 pages
    • dimensions: 229 x 152 x 10 mm
    • weight: 0.234kg
    • availability: Available
  • Table of Contents

    1. The existence theorem
    Appendix: the integrity theorem for network flows
    2. The parallelogram property
    Appendix: the binary perfect code theorem
    Appendix: association schemes and metrically regular graphs
    3. Steiner points and Veblen points
    Appendix: Steiner systems
    4. Minimal edge-colourings of complete graphs
    Appendix: latin squares, SDRs and permanents
    5. Biplanes and metric regularity
    Appendix: symmetric designs
    6. Automorphism groups
    Appendix: multiply transitive groups
    7. Resolutions and partition systems

  • Author

    Peter J. Cameron

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