Handbook of Combinatorial Designs
This page contains acknowledgments by individual authors and the editors
for assistance with the CRC Handbook of Combinatorial Designs, edited by
CRC Press, Boca Raton FL, 1996.
CRC Handbook of Combinatorial Designs, General Acknowledgments
from the editors-in-chief
Acknowledgments are due to many individuals. We must begin by
acknowledging the excellent work done by the contributors.
Their job was made difficult by the style and length
restrictions placed upon them. Many had written hundreds of
pages on their topic, yet were asked to summarize in
a few pages. They also were asked to do this within the fairly rigid
stylistic framework that is consistent now throughout the book. The
editors were merciless in their attempt to uphold this style. Many
chapters were edited extensively. We thank the authors for their
Most chapters have
profited from comments from a wide variety of readers,
in addition to the authors and editors.
Acknowledgments for assistance on individual chapters are
lengthy, and are available on this page.
A compilation of this size can only be accomplished with the help of a small
army of people. We were fortunate to have a helpful group of advisory
editors, and excellent technical support from CRC Press, and the Universities
of Vermont and Waterloo.
We give special thanks to
help in the area of statistical designs and to Vladimir Tonchev for
expert advice on coding theory. Special thanks
also go to Dan Archdeacon and to Norm Finizio who proofread much of the
In addition, for their support in compiling this handbook, we thank
Julian Abel, Frank Bennett,
Ron Mullin, Bob Stern,
John van Rees,
Wayne Yuhasz, and of course Hal and Daisy.
We thank our wives, Sue Dinitz and Karen Colbourn,
and our children, Mike,
Amy, and Tommy Dinitz and Susie Colbourn, for
their support and love despite the many long hours that it took to
assemble this handbook. At times we tried their patience,
but they understood.
Part I: Balanced Incomplete Block Designs and t-Designs
- 2-(v, k, \lambda ) Designs of Small Order (
- BIBDs with Small Block Size (R. Julian R. Abel, Malcolm Greig):
- t-Designs, t \geq 3
( Donald L. Kreher):
- Steiner Systems (
Charles J. Colbourn ,
Thanks to Ian Blake,
Andries Brouwer, and
for references and helpful comments.
- Symmetric Designs (Tran van Trung):
- Resolvable and Near Resolvable Designs (R. Julian R. Abel, Steven C. Furino):
Part II: Latin Squares, MOLS, and Orthogonal Arrays
- Latin Squares ( Charles J. Colbourn , Jeffrey H. Dinitz ):
Thanks to Frank Bennett, Donald Keedwell, Donald Preece, Peter Rodney,
Rees, and Zhu Lie for their assistance.
- Mutually Orthogonal Latin Squares (MOLS) (R. Julian R. Abel, Andries
E. Brouwer, Charles
J. Colbourn , Jeffrey
H. Dinitz ): The computation of a new table of bounds for
MOLS, and for incomplete MOLS, was assisted by a large number of
people in addition to the four authors. Foremost among these were
Frank Bennett, Ron Mullin, Yin Jianxing, Hantao Zhang, and Zhu Lie.
Valuable assistance was also provided by Jo Ellis-Monaghan, Anthony
Evans, Malcolm Greig, Esther Lamken, Alan Ling, Gary
Mullen, Peter Owens, Donald Preece, Paul Schellenberg, Doug Stinson, Rick Wilson,
Miecyzslaw Wojtas, and Xiaojun Zhu.
- Incomplete MOLS (R. Julian R. Abel, Charles J. Colbourn , Jeffrey H. Dinitz ):
See MOLS above.
- Orthogonal Arrays of Index More Than One ( Charles J. Colbourn ):
and Yin Jianxing
for pointing out references and for general comments.
- Orthogonal Arrays of Strength More Than Two
Charles J. Colbourn ):
Thanks especially to Dieter Jungnickel, Neil Sloane and Doug Stinson for
pointing out relevant work.
Part III: Pairwise Balanced Designs
- PBDs and GDDs: The Basics (Ronald C. Mullin, Hans-Dietrich O.F. Gronau):
The authors are indebted to many individuals for their assistance in
the preparation of this chapter. In particular we thank Zhu Lie,
Jianxing Yin, Charlie Colbourn,
and Jeffrey Higham for their
many contributions. Special thanks are due to Marg Feeney for her
skilled preparation of the document.
Their support was greatly
- PBDs: Recursive Constructions (Ronald C. Mullin, Hans-Dietrich O.F. Gronau):
- PBD-Closure (Frank E. Bennett, Hans-Dietrich O.F. Gronau,
Alan C.H. Ling, Ronald C. Mullin): The authors would like to acknowledge the support of NATO-grant CRG 940085.
- Pairwise Balanced Designs as Linear Spaces (Hans-Dietrich O.F. Gronau, Ronald C. Mullin, Christian Pietsch):
- PBDs and GDDs of Higher Index (Ronald C. Mullin, Hans-Dietrich O.F. Gronau):
- PBDs, Frames, and Resolvability (Ronald C. Mullin, Hans-Dietrich O.F. Gronau):
Part IV: Other Combinatorial Designs
- Association Schemes (Christopher D. Godsil):
- Balanced (Part) Ternary Designs (Thomas Kunkle, Dinesh G. Sarvate):
- Balanced Tournament Designs (Esther R. Lamken):
- Bhaskar Rao Designs (Warwick de Launey):
- Complete Mappings and Sequencings of Finite Groups (Donald Keedwell):
- Configurations (Harald Gropp):
- Costas Arrays (Herbert Taylor):
- Coverings ( Douglas R. Stinson):
- Cycle Systems (C.A. Rodger):
- Difference Families (R. Julian R. Abel):
- Difference Matrices ( Charles J. Colbourn , Warwick de Launey):
for their assistance.
- Difference Sets: Abelian (Dieter Jungnickel, Alexander Pott):
- Difference Sets: Nonabelian (Ken W. Smith):
The author thanks
Robert A. Liebler (Colorado State University) who has made numerous
contributions in the area of nonabelian difference sets which, due to
space, are not explicitly recognized in the chapter.
- Difference Triangle Sets ( Charles J. Colbourn ):
Nabil Shalaby brought the importance of this area to my attention, and
provided a number of useful references. Thanks also to
Yeow Meng Cheeand
Alex Rosa for providing additional materials.
- Directed Designs (Frank E. Bennett, Alireza Mahmoodi):
- D-Optimal Matrices (Hadi Kharaghani):
- Embedding Partial Quasigroups
- Equidistant Permutation Arrays (Alireza Mahmoodi, Paul J. Schellenberg):
- Factorial Designs ( Deborah J. Street):
- Frequency Squares (Charles F. Laywine):
The author would like to thank Gary L. Mullen for his help on this section.
- Generalized Quadrangles
(Stanley E. Payne):
- Graph Decompositions and Designs
Many thanks to Jiping Liu and Joseph Yu for their invaluable assistance in preparing this section.
- Graphical Designs
(Yeow Meng Chee):
- Hadamard Matrices and Designs (R. Craigen):
- Hall Triple Systems (Lucien Beneteau):
- Howell Designs ( Jeffrey H. Dinitz):
- Maximal Sets of MOLS (Anthony B. Evans):
- Mendelsohn Designs
Thanks to Frank Bennet and Zhu Lie for corrections and updates.
- The Oberwolfach Problem (
- Ordered Designs and Perpendicular Arrays
- Orthogonal Designs (Jennifer Seberry, R. Craigen):
- Orthogonal Main Effect Plans ( Deborah J. Street):
- Packings ( Douglas R. Stinson):
- Partial Geometries (Joseph A. Thas):
- Partially Balanced Incomplete Block Designs
( Deborah J. Street,
Anne Penfold Street ):
- Quasigroups (Frank E. Bennett):
- Quasi-Symmetric Designs (Mohan S. Shrikhande):
The author acknowledges support of Central
Michigan University FRCE grant #42943.
- (r, \lambda )-designs
(G.H. John van Rees):
The author would like to thank Ron Mullin and
- Room Squares ( Jeffrey H. Dinitz ):
Thanks to Charlie Colbourn for helping on this section;
the first section written for this handbook.
- Self-Orthogonal Latin Squares (SOLS) (L. Zhu):
- SOLS with a Symmetric Orthogonal Mate (SOLSSOM) (Norman J. Finizio):
- Sequences with Zero Autocorrelation (Christos Koukouvinos):
- Skolem Sequences (Nabil Shalaby):
- Spherical t-Designs (Stuart G. Hoggar):
- Starters ( Jeffrey H. Dinitz ):
- Trades and Defining Sets
(Anne Penfold Street ):
- (t,m,s)-Nets ( Charles J. Colbourn ):
Mark Lawrence kindly provided much material in this area. In addition,
gave numerous helpful comments.
- Tuscan Squares (Hong-Yeop Song,
Jeffrey H. Dinitz ):
The second author would like to thank Herb Taylor for introducing him to
the first author.
- t-Wise Balanced Designs (Earl S. Kramer):
- Uniformly Resolvable Designs (Peter Danziger, Peter Rodney):
- Vector Space Designs (Dijen K. Ray-Chaudhuri):
- Weighing Matrices and Conference Matrices (R. Craigen):
- Whist Tournaments (Ian Anderson):
- Youden Designs, Generalized
( Charles J. Colbourn ):
Thanks to Sam Hedayat for providing literature on this topic.
- Youden Squares (Donald A. Preece):
Part V: Applications
- Codes (Vladimir D. Tonchev):
- Computer Science: Selected Applications ( Charles J. Colbourn ):
Thanks especially to Paul van Oorschot, with whom a lengthier survey
on this subject was published in 1989. Thanks also to
Yeow Meng Chee,
K. Gopalakrishnan, and Doug Stinson for helpful comments.
- Applications of Designs to Cryptography (K. Gopalakrishnan, Douglas R. Stinson):
- Derandomization (K. Gopalakrishnan, Douglas R. Stinson):
- Optimality and Efficiency: Comparing Block Designs ( Deborah J. Street):
- Group Testing ( Charles J. Colbourn ):
Thanks to Prof. Raghavarao for kindly providing related literature.
Thanks also to
Yeow Meng Chee for helpful comments.
- Scheduling a Tournament ( Jeffrey H. Dinitz , Esther R. Lamken, Walter D. Wallis ):
- Winning the Lottery ( Charles J. Colbourn ):
A great many people educated me about this subject. Having never bought
a lottery ticket in my life, their nuances were a mystery to me.
Dom de Caen,
and John van Rees
for their assistance.
Part VI: Related Mathematics and Computational Methods
- Finite Groups and Designs (Leo G. Chouinard II, Robert Jajcay,
Spyros S. Magliveras):
- Number Theory and Finite Fields (Hugh Williams):
[The editors would like to thank Dave Dummit and Brett Tangedal for their assistance with this section.]
- Graphs and Multigraphs
(Gordon F. Royle):
The author wishes to thank Brendan McKay and Gunnar Brinkmann
for their help in compiling this section. [The editors would like to thank
Dan Archdeacon for his useful comments here also.]
- Factorizations of Graphs (Lars D. Andersen):
- Strongly Regular Graphs (Andries E. Brouwer):
- Two-Graphs (Edward Spence):
In his writing of this section the author was greatly
influenced by the papers of J. J. Seidel cited in the references.
These have been of not inconsiderable importance in the development of
the theory of two-graphs. He also gratefully acknowledges the
assistance given by F. C. Bussemaker and
much of the data on two-graphs that appears on the home page.
- Classical Geometries
- Projective Planes, Nondesarguesian (Marialuisa J. de Resmini):
- Computational Methods in Design Theory (Peter B. Gibbons):
The author wishes to thank the following for their encouraging comments and
many helpful suggestions concerning various drafts of this section:
Leo Chouinard, Charlie Colbourn ,
Jeff Dinitz , David Garnick, Curt Hjorring,
Spyros S. Magliveras,
Christian Pietsch, Doug Stinson.
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