Parallelisms of complete designs
Author(s)
Bibliographic Information
Parallelisms of complete designs
（London Mathematical Society lecture note series, 23）
Cambridge University Press, 1976
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Hokkaido University, Library, Graduate School of Science, Faculty of Science and School of Science図書
dc19:510/l8462020927278
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Description and Table of Contents
Description
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.
Table of Contents
- Introduction
- 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
- Bibliography
- Index.
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