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Triple Systems : Oxford Mathematical Monographs - Charles Colbourn

Triple Systems

Oxford Mathematical Monographs

Hardcover Published: 1st March 1999
ISBN: 9780198535768
Number Of Pages: 576

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Triple systems are among the simplest combinatorial designs, and are a natural generalization of graphs. They have connections with geometry, algebra, group theory, finite fields, and cyclotomy; they have applications in coding theory, cryptography, computer science, and statistics. Triple systems provide in many cases the prototype for deep results in combinatorial design theory; this design theory is permeated by problems that were first understood in the context of triple systems and then generalized. Such a rich set of connections has made the study of triple systems an extensive, but sometimes disjointed, field of combinatorics. This book attempts to survey current knowledge on the subject, to gather together common themes, and to provide an accurate portrait of the huge variety of problems and results. Representative samples of the major syles of proof technique are included, as is a comprehensive bibliography.

"This magnificent bible on triple systems should belong on the shelves of everyone who works in triple systems and block designs. It will be a useful reference text for people in allied fields such as graph theory and cryptography. The level of the text is aimed at graduate and research use, although some chapters could be used as a basis for an honours student's project. . . . [J]ust about every other aspect of triple systems gets a mention somewhere in this great book, and the bibliography is sufficiently complete that it mentions related work not covered in the text." -- Mathematical Reviews "This magnificent bible on triple systems should belong on the shelves of everyone who works in triple systems and block designs. It will be a useful reference text for people in allied fields such as graph theory and cryptography. The level of the text is aimed at graduate and research use, although some chapters could be used as a basis for an honours student's project. . . . [J]ust about every other aspect of triple systems gets a mention somewhere in this great book, and the bibliography is sufficiently complete that it mentions related work not covered in the text." -- Mathematical Reviews "This magnificent bible on triple systems should belong on the shelves of everyone who works in triple systems and block designs. It will be a useful reference text for people in allied fields such as graph theory and cryptography. The level of the text is aimed at graduate and research use, although some chapters could be used as a basis for an honours student's project. . . . [J]ust about every other aspect of triple systems gets a mention somewhere in this great book, and the bibliography is sufficiently complete that it mentions related work not covered in the text." -- Mathematical Reviews "This magnificent bible on triple systems should belong on the shelves of everyone who works in triple systems and block designs. It will be a useful reference text for people in allied fields such as graph theory and cryptography. The level of the text is aimed at graduate and research use, although some chapters could be used as a basis for an honours student's project. . . . [J]ust about every other aspect of triple systems gets a mention somewhere in this great book, and the bibliography is sufficiently complete that it mentions related work not covered in the text." -- MathematicalReviews

Historical introduction 1: Design-theoretic fundamentals 2: Existence: direct methods 3: Existence:recursive methods 4: Isomorphism and invariants 5: Enumeration 6: Subsystems and holes 7: Automorphisms I: small groups 8: Automorphisms II: large groups 9: Leaves and partial tripls systems 10: Excesses and coverings 11: Embedding and its variants 12: Neighbourhoods 13: Configurations 14: Intersections 15: Large sets and partitions 16: Support sizes 17: Independent sets 18: Chromatic number 19: Chromatic index and resolvability 20: Orthogonal resolutions 21: Nested and derived triple systems 22: Decomposability 23: Directed triple systems 24: Mendelsohn triple systems Bibliographies Index

ISBN: 9780198535768
ISBN-10: 0198535767
Series: Oxford Mathematical Monographs
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 576
Published: 1st March 1999
Publisher: Oxford University Press
Country of Publication: GB
Dimensions (cm): 24.1 x 16.2  x 3.8
Weight (kg): 0.99

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