Parallelisms of complete designs / Peter J. Cameron.

Format:

Book

Author/Creator:

Cameron, Peter J. (Peter Jephson), 1947- author.

Series:

London Mathematical Society lecture note series ; 23.

London Mathematical Society lecture note series ; 23

Language:

English

Subjects (All):

Combinatorial designs and configurations.

Permutation groups.

Parallels (Geometry).

Physical Description:

1 online resource (144 pages) : digital, PDF file(s).

Place of Publication:

Cambridge : Cambridge University Press, 1976.

Language Note:

English

Summary:

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.

Contents:

Cover; Title; Copyright; Contents; Introduction; 1 The existence theorem; APPENDIX 1A. The Integrity Theorem for network flows; 2 The parallelogram property; APPENDIX 2A. The binary perfect code theorem; APPENDIX 2B. Association schemes and metrically regular graphs; 3 Steiner points and Veblen points; APPENDIX 3A. Steiner systems; 4 Edge-colourings of complete graphs; APPENDIX 4A. Latin squares, SDRs, and permanents; 5 Biplanes and metric regularity; APPENDIX 5A. Symmetric designs; 6 Automorphism groups; APPENDIX 6A. Multiply transitive groups; 7 Resolutions and partition systems

BibliographyBooks; Papers; Index

Notes:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Includes bibliographical references and index.

ISBN:

1-139-88369-0

1-107-36575-9

1-107-37048-5

1-107-36084-6

1-107-36838-3

1-299-40356-5

1-107-36329-2

0-511-66210-6