Parallelisms of Complete Designs

Peter J. Cameron

doi:10.1017/CBO9780511662102

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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Parallelisms of Complete Designs

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Contents

Frontmatter
pp i-ii

Contents
pp iii-iv

Introduction
pp 1-3

1 - The existence theorem
pp 4-18

2 - The parallelogram property
pp 19-45

3 - Steiner points and Veblen points
pp 46-62

4 - Minimal edge-colourings of complete graphs
pp 63-80

5 - Biplanes and metric regularity
pp 81-107

6 - Automorphism groups
pp 108-128

7 - Resolutions and partition systems
pp 129-137

Bibliography
pp 138-142

Index
pp 143-144

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Parallelisms of Complete Designs

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