Handbook of Combinatorial Designs, Second Edition

by Colbourn; Charles J.

• ISBN13: 9781584885061
• ISBN10: 1584885068
• Edition: 2nd
• Format: Hardcover
• Copyright: 2006-11-02
• Publisher: Chapman & Hall/

Summary

Continuing in the bestselling, informative tradition of the first edition, the Handbook of Combinatorial Designs, Second Edition remains the only resource to contain all of the most important results and tables in the field of combinatorial design. This handbook covers the constructions, properties, and applications of designs as well as existence results.Over 30% longer than the first edition, the book builds upon the groundwork of its predecessor while retaining the original contributors' expertise. The first part contains a brief introduction and history of the subject. The following parts focus on four main classes of combinatorial designs: balanced incomplete block designs, orthogonal arrays and Latin squares, pairwise balanced designs, and Hadamard and orthogonal designs. Closely connected to the preceding sections, the next part surveys 65 additional classes of designs, such as balanced ternary, factorial, graphical, Howell, quasi-symmetric, and spherical. The final part presents mathematical and computational background related to design theory.New to the Second Edition· An introductory part that provides a general overview and a historical perspective of the area· New chapters on the history of design theory, various codes, bent functions, and numerous types of designs· Fully updated tables, including BIBDs, MOLS, PBDs, and Hadamard matrices· Nearly 2,200 references in a single bibliographic sectionMeeting the need for up-to-date and accessible tabular and reference information, this handbook provides the tools to understand combinatorial design theory and applications that span the entire discipline.

Table of Contents

Introduction
Opening the Door	3	(8)
Charles J. Colbourn
Design Theory: Antiquity to 1950	11	(14)
Ian Anderson
Charles J. Colbourn
Jeffrey H. Dinitz
Terry S. Griggs
Block Designs
2-(ν, κ, lambda;) Designs of Small Order	25	(33)
Rudolf Mathon
Alexander Rosa
Triple Systems	58	(14)
Charles J. Colbourn
BIBDs with Small Block Size	72	(7)
R. Julian R. Abel
Malcolm Greig
t-Designs with t ≥ 3	79	(23)
Gholamreza B. Khosrovshahi
Reinhard Laue
Steiner Systems	102	(8)
Charles J. Colbourn
Rudolf Mathon
Symmetric Designs	110	(14)
Yury J. Ionin
Tran van Trung
Resolvable and Near-Resolvable Designs	124	(11)
R. Julian R. Abel
Gennian Ge
Jianxing Yin
Latin Squares
Latin Squares	135	(17)
Charles J. Colbourn
Jeffrey H. Dinitz
Ian M. Wanless
Quasigroups	152	(8)
Frank E. Bennett
Charles C. Lindner
Mutually Orthogonal Latin Squares (MOLS)	160	(33)
R. Julian R. Abel
Charles J. Colbourn
Jeffrey H. Dinitz
Incomplete MOLS	193	(18)
R. Julian R. Abel
Charles J. Colbourn
Jeffrey H. Dinitz
Self-Orthogonal Latin Squares (SOLS)	211	(8)
Norman J. Finizio
L. Zhu
Orthogonal Arrays of Index More Than One	219	(5)
Malcolm Greig
Charles J. Colbourn
Orthogonal Arrays of Strength More Than Two	224	(7)
Charles J. Colbourn
Pairwise Balanced Designs
PBDs and GDDs: The Basics	231	(5)
Ronald C. Mullin
Hans-Dietrich O. F. Gronau
PBDs: Recursive Constructions	236	(11)
Malcolm Greig
Ronald C. Mullin
PBD-Closure	247	(8)
R. Julian R. Abel
Frank E. Bennett
Malcolm Greig
Group Divisible Designs	255	(6)
Gennian Ge
PBDs, Frames, and Resolvability	261	(5)
Gennian Ge
Ying Miao
Pairwise Balanced Designs as Linear Spaces	266	(7)
Anton Betten
Hadamard Matrices and Related Designs
Hadamard Matrices and Hadamard Designs	273	(7)
Robert Craigen
Hadi Kharaghani
Orthogonal Designs	280	(16)
Robert Craigen
Hadi Kharaghani
D-Optimal Matrices	296	(3)
Hadi Kharaghani
William Orrick
Bhaskar Rao Designs	299	(2)
Warwick de Launey
Generalized Hadamard Matrices	301	(5)
Warwick de Launey
Balanced Generalized Weighing Matrices and Conference Matrices	306	(7)
Yury J. Ionin
Hadi Kharaghani
Sequence Correlation	313	(4)
Tor Helleseth
Complementary, Base, and Turyn Sequences	317	(4)
Hadi Kharaghani
Christos Koukouvinos
Optical Orthogonal Codes	321	(4)
Tor Helleseth
Other Combinatorial Designs
Association Schemes	325	(5)
Christopher D. Godsil
Sung Y. Song
Balanced Ternary Designs	330	(3)
Spencer P. Hurd
Dinesh G. Sarvate
Balanced Tournament Designs	333	(4)
Esther R. Lamken
Bent Functions	337	(2)
Douglas R. Stinson
Block-Transitive Designs	339	(6)
Anne Delandtsheer
Complete Mappings and Sequencings of Finite Groups	345	(8)
Anthony B. Evans
Configurations	353	(2)
Harald Gropp
Correlation-immune and Resilient Functions	355	(2)
K. Gopalakrishnan
Douglas R. Stinson
Costas Arrays	357	(4)
Herbert Taylor
Jeffrey H. Dinitz
Covering Arrays	361	(4)
Charles J. Colbourn
Coverings	365	(8)
Daniel M. Gordon
Douglas R. Stinson
Cycle Decompositions	373	(9)
Darryn Bryant
Chris Rodger
Defining Sets	382	(3)
Ken Gray
Anne Penfold Street
Deletion-correcting Codes	385	(4)
Vladimir I. Levenshtein
Derandomization	389	(3)
K. Gopalakrishnan
Douglas R. Stinson
Difference Families	392	(19)
R. Julian R. Abel
Marco Buratti
Difference Matrices	411	(8)
Charles J. Colbourn
Difference Sets	419	(17)
Dieter Jungnickel
Alexander Pott
Ken W. Smith
Difference Triangle Sets	436	(5)
James B. Shearer
Directed Designs	441	(4)
Frank E. Bennett
Alireza Mahmoodi
Factorial Designs	445	(20)
Deborah J. Street
Frequency Squares and Hypercubes	465	(7)
Charles F. Laywine
Gary L. Mullen
Generalized Quadrangles	472	(5)
Stanley E. Payne
Graph Decompositions	477	(9)
Darryn Bryant
Saad El-Zanati
Graph Embeddings and Designs	486	(4)
Jozef Siran
Graphical Designs	490	(4)
Yeow Meng Chee
Donald L. Kreher
Grooming	494	(2)
Jean-Claude Bermond
David Coudert
Hall Triple Systems	496	(3)
Lucien Beneteau
Howell Designs	499	(5)
Jeffrey H. Dinitz
Infinite Designs	504	(2)
Peter J. Cameron
Bridget S. Webb
Linear Spaces: Geometric Aspects	506	(6)
Lynn Margaret Batten
Lotto Designs	512	(7)
(Ben) P. C. Li
G. H. John van Rees
Low Density Parity Check Codes	519	(5)
Ian F. Blake
Magic Squares	524	(4)
Joseph M. Kudrle
Sarah B. Menard
Mendelsohn Designs	528	(7)
Eric Mendelsohn
Nested Designs	535	(5)
J. P. Morgan
Optimality and Efficiency: Comparing Block Designs	540	(3)
Deborah J. Street
Ordered Designs, Perpendicular Arrays, and Permutation Sets	543	(4)
Jurgen Bierbrauer
Orthogonal Main Effect Plans	547	(3)
Deborah J. Street
Packings	550	(7)
Douglas R. Stinson
Ruizhong Wei
Jianxing Yin
Partial Geometries	557	(5)
Joseph A. Thas
Partially Balanced Incomplete Block Designs	562	(4)
Deborah J. Street
Anne Penfold Street
Perfect Hash Families	566	(2)
Robert A. Walker II
Charles J. Colbourn
Permutation Codes and Arrays	568	(4)
Peter J. Dukes
Permutation Polynomials	572	(2)
Gary L. Mullen
Pooling Designs	574	(2)
David C. Torney
Quasi-3 Designs	576	(2)
Gary McGuire
Quasi-Symmetric Designs	578	(4)
Mohan S. Shrikhande
(r, λ)-designs	582	(2)
G. H. John van Rees
Room Squares	584	(7)
Jeffrey H. Dinitz
Scheduling a Tournament	591	(15)
J. H. Dinitz
Dalibor Froncek
Esther R. Lamken
Walter D. Wallis
Secrecy and Authentication Codes	606	(6)
K. Gopalakrishnan
Douglas R. Stinson
Skolem and Langford Sequences	612	(5)
Nabil Shalaby
Spherical Designs	617	(5)
Akihiro Munemasa
Starters	622	(7)
Jeffrey H. Dinitz
Superimposed Codes and Combinatorial Group Testing	629	(4)
Charles J. Colbourn
Frank K. Hwang
Supersimple Designs	633	(2)
Hans-Dietrich O. F. Gronau
Threshold and Ramp Schemes	635	(4)
K. Gopalakrishnan
Douglas R. Stinson
(t,m,s)-Nets	639	(5)
William J. Martin
Trades	644	(5)
A. S. Hedayat
Gholamreza B. Khosrovshahi
Turan Systems	649	(3)
Miklos Ruszinko
Tuscan Squares	652	(5)
Wensong Chu
Solomon W. Golomb
Hong-Yeop Song
t-Wise Balanced Designs	657	(6)
Earl S. Kramer
Donald L. Kreher
Whist Tournaments	663	(5)
Ian Anderson
Norman J. Finizio
Youden Squares and Generalized Youden Designs	668	(9)
Donald A. Preece
Charles J. Colbourn
Related Mathematics
Codes	677	(25)
Vladimir D. Tonchev
Finite Geometry	702	(27)
Leo Storme
Divisible Semiplanes	729	(2)
Rudolf Mathon
Graphs and Multigraphs	731	(9)
Gordon F. Royle
Factorizations of Graphs	740	(15)
Lars D. Andersen
Computational Methods in Design Theory	755	(28)
Peter B. Gibbons
Patric R. J. Ostergard
Linear Algebra and Designs	783	(8)
Peter J. Dukes
Richard M. Wilson
Number Theory and Finite Fields	791	(28)
Jeffrey H. Dinitz
Hugh C. Williams
Finite Groups and Designs	819	(28)
Leo G. Chouinard II
Robert Jajcay
Spyros S. Magliveras
Designs and Matroids	847	(5)
Peter J. Cameron
Michel M. Deza
Strongly Regular Graphs	852	(16)
Andries E. Brouwer
Directed Strongly Regular Graphs	868	(7)
Andries E. Brouwer
Sylvia A. Hobart
Two-Graphs	875	(8)
Edward Spence
Bibliography and Index
Bibliography	883	(84)
Index	967