Parallelisms of Complete Designs

by Peter J. Cameron

Overview

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.

Product Details

ISBN-13:	9780521211604
Publisher:	Cambridge University Press
Publication date:	06/10/1976
Series:	London Mathematical Society Lecture Note Series , #23
Pages:	152
Product dimensions:	5.98(w) x 9.02(h) x 0.39(d)

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.