Handbook of combinatorial designs /

Handbook of combinatorial designs /

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Continuing in the bestselling, informative tradition of the first edition, this second edition remains the only resource to contain all of the most important results and tables in the area of combinatorial design. The handbook covers the constructions of designs, existence results, properties of des...

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Bibliographic Details
Corporate Author: Taylor & Francis
Other Authors: Colbourn, C. J (Charles J.), 1953-, Dinitz, Jeffrey H., 1952-
Format: Book
Language:English
Published: Boca Raton, FL : Chapman & Hall/Taylor & Francis, ©2007
Edition:2nd ed
Series:Discrete mathematics and its applications
Subjects:
Combinatorial designs and configurations
Kombinatorik
MATHEMATICS > Combinatorics
Combinatieleer
Electronic books
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Table of Contents:
  • 21. Factorial designs / Deborah J. Street
  • 22. Frequency squares and hypercubes / Charles F. Laywine and Gary L. Mullen
  • 23. Generalized quadrangles / Stanley E. Payne
  • 24. Graph decompositions / Darryn Bryant and Saad El-Zanati
  • 25. Graph embeddings and designs / Jozef Siran
  • 26. Graphical designs / Yeow Meng Chee and Donald L. Kreher
  • 27. Grooming / Jean-Claude Bermond and David Coudert
  • 28. Hall triple systems / Lucien Beneteau
  • 29. Howell designs / Jeffrey H. Dinitz
  • 30. Infinite designs / Peter J. Cameron and Briget S. Webb
  • 31. Linear spaces : geometric aspects / Lynn Margaret Batten
  • 32. Lotto designs / (Ben) P.C. Li and G.H. John van Rees
  • 33. Low density parity check codes / Ian F. Blake
  • 34. Magic squares / Joseph M. Kudrle and Sarah B. Menard
  • 35. Mendelsohn designs / Eric Mendelsohn
  • 36. Nested designs / J.P. Morgan
  • 37. Optimality and efficiency : comparing block designs / Deborah J. Street
  • 38. Ordered designs, perpendicular arrays, and permutation sets / Jurgen Bierbrauer
  • 39. Orthogonal main effect plans / Deborah J. Street
  • 40. Packings / Douglas R. Stinson, Ruizhong Wei and Jianxing Yin
  • 41. Partial geometries / Joseph A. Thas
  • 42. Partially balanced incomplete block designs / Deborah J. Street and Anne Penfold Street
  • 43. Perfect hash families / Robert A. Walker II and Charles J. Colbourn
  • 44. Permutation codes and arrays / Peter J. Dukes
  • 45. Permutation polynomials / Gary L. Mullen
  • 46. Pooling designs / David C. Torney
  • 47. Quasi-3 designs / Gary McGuire
  • 48. Quasi-symmetric designs / Mohan S. Shrikhande
  • 49. (r, [lambda])-designs / G.H. John van Rees
  • 50. Room squares / Jeffrey H. Dinitz
  • 3. D-optimal matrices / Hadi Kharaghani and William Orrick
  • 4. Bhaskar Rao designs / Warwick de Launey
  • 5. Generalized hadamard matrices / Warwick de Launey
  • 6. Balanced generalized weighing matrices and conference matrices / Yury J. Ionin and Hadi Kharaghani
  • 7. Sequence correlation / Tor Helleseth
  • 8. Complementary, base, and turyn sequences / Hadi Kharaghani and Curistos Koukouvinos
  • 9. Optical orthogonal codes / Tor Helleseth
  • VI. Other combinatorial designs
  • 1. Association schemes / Christopher D. Godsil and Sung Y. Song
  • 2. Balanced ternary designs / Spencer P. Hurd and Dinesh G. Sarvate
  • 3. Balanced tournament designs / Esther R. Lamken
  • 4. Bent functions / Douglas R. Stinson
  • 5. Block-transitive designs / Anne Delandtsheer
  • 6. Complete mappings and sequencings of finite groups / Anthony B. Evans
  • 7. Configurations / Harald Gropp
  • 8. Correlation-immune and resilient functions / K. Gopalakrishnan and Douglas R. Stinson
  • 9. Costas arrays / Herbert Taylor and Jeffrey H. Dinitz
  • 10. Covering arrays / Charles J. Colbourn
  • 11. Coverings / Daniel M. Gordon and Douglas R. Stinson
  • 12. Cycle decompositions / Darryn Bryant and Chris Rodger
  • 13. Defining sets / Ken Gray and Anne Penfold Street
  • 14. Deletion-correcting codes / Vladimir L. Levenshtein
  • 15. Derandomization / K. Gopalakrishnan and Douglas R. Stinson
  • 16. Difference families / R. Julian R. Abel and Marco Buratti
  • 17. Difference matrices / Charles J. Colbourn
  • 18. Difference sets / Dieter Jungnickel, Alexander Pott and Ken W. Smith
  • 19. Difference triangle sets / James B. Shearer
  • 20. Directed designs / Frank E. Bennett and Alireza Mahmoodi
  • 51. Scheduling a tournament / J.H. Dinitz, Dalibor Froncek, Esther R. Lamken and Walter D. Wallis
  • 52. Secrecy and authentication codes / K. Gopalakrishnan and Douglas R. Stinson
  • 53. Skolem and langford sequences / Nabil Shalaby
  • 54. Spherical designs / Akihiro Munemasa
  • 55. Starters / Jeffrey H. Dinitz
  • 56. Superimposed codes and combinatorial group testing / Charles J. Colbourn and Frank K. Hwang
  • 57. Supersimple designs / Hans-Dietrich O.F. Gronau
  • 58. Threshold and ramp schemes / K. Gopalakrishnan and Douglas R. Stinson
  • 59. (t, m, s)-nets / William J. Martin
  • 60. Trades / A.S. Hedayat and Gholamreza B. Khosrovshahi
  • 61. Turan systems / Miklos Ruszinko
  • 62. Tuscan squares / Wensong Chu, Solomon W. Golomb and Hong-Yeop Song
  • 63. t-wise balanced designs / Earl S. Kramer and Donald L. Kreher
  • 64. Whist tournaments / Ian Anderson and Norman J. Finizio
  • 65. Youden squares and generalized youden designs / Donald A. Preece and Charles J. Colbourn
  • VII. Related mathematics
  • 1. Codes / Vladimir D. Tonchev
  • 2. Finite geometry / Leo Storme
  • 3. Divisible semiplanes / Rudolf Mathon
  • 4. Graphs and multigraphs / Gordon F. Royle
  • 5. Factorizations of graphs / Lars D. Andersen
  • 6. Computational methods in design theory / Peter B. Gibbons and Patric R.J. Ostergard
  • 7. Linear algebra and designs / Peter J. Dukes and Richard M. Wilson
  • 8. Number theory and finite fields / Jeffrey H. Dinitz and Hugh C. Williams
  • 9. Finite groups and designs / Leo G. Chouinard II, Robert Jajcay and Spyros S. Magliveras
  • 10. Designs and matroids / Peter J. Cameron and Michel M. Deza
  • 11. Strongly regular graphs / Andries E. Brouwer
  • 12. Directed strongly regular graphs / Andries E. Brouwer and Sylvia A. Hobart
  • 13. Two-graphs / Edward Spence
  • I. Introduction
  • 1. Opening the door / Charles J. Colbourn
  • 2. Design theory : antiquity to 1950 / Ian Anderson, Charles J. Colbourn, Jeffrey H. Dinitz and Terry S. Giuggs
  • II. Block designs
  • 1. 2-(v, k, [lambda]) designs of small order / Rudolf Mathon and Alexander Itosa
  • 2. Triple systems / Charles J. Colbourn
  • 3. BIBDs with small block size / R. Julian R. Abel and Malcolm Greig
  • 4. t-designs with t [actual symbol not reproducible] 3 / Gholamreza B. Khosrovshahi and Reinhard Laue
  • 5. Steiner systems / Charles J. Colbourn and Rudolf Mathon
  • 6. Symmetric designs / Yury J. Ionin and Tran Van Trung
  • 7. Resolvable and near-resolvable designs / R. Julian R. Abel, Gennian Ge and Jianxing Yin
  • III. Latin squares
  • 1. Latin squares / Charles J. Colbourn, Jeffrey H. Dinitz and Ian M. Wanless
  • 2. Quasigroups / Frank E. Bennett and Charles C. Lindner
  • 3. Mutually orthogonal latin squares (MOLS) / R. Julian R. Abel, Charles J. Colbourn and Jeffrey H. Dinitz
  • 4. Incomplete MOLS / R. Julian R. Abel, Charles J. Colbourn and Jeffrey H. Dinitz
  • 5. Self-orthogonal latin squares (SOLS) / Norman J. Finizio and L. Zhu
  • 6. Orthogonal arrays of index more than one / Malcolm Greig and Charles J. Colbourn
  • 7. Orthogonal arrays of strength more than two / Charles J. Colbourn
  • IV. Pairwise balanced designs
  • 1. PBDs and GDDs : the basics / Ronald C. Mullin and Hans-Dietrich O.F. Gronau
  • 2. PBDs : recursive constructions / Malcolm Greig and Ronald C. Mullin
  • 3. PBD-closure / R. Julian R. Abel, Frank E. Bennett and Malcolm Greig
  • 4. Group divisible designs / Gennian Ge
  • 5. PBDs, frames, and resolvability / Gennian Ge and Ying Miao
  • 6. Pairwise balanced designs as linear spaces / Anton Betten
  • V. Hadamard matrices and related designs
  • 1. Hadamard matrices and hadamard designs / Robert Craigen and Hadi Kharaghani
  • 2. Orthogonal designs / Robert Craigen and Hadi Kharaghani
  • I. Introduction
  • 1. Opening the door / Charles J. Colbourn
  • 2. Design theory : antiquity to 1950 / Ian Anderson, Charles J. Colbourn, Jeffrey H. Dinitz and Terry S. Giuggs
  • II. Block designs
  • 1. 2-(v, k, λ) designs of small order / Rudolf Mathon and Alexander Itosa
  • 2. Triple systems / Charles J. Colbourn
  • 3. BIBDs with small block size / R. Julian R. Abel and Malcolm Greig
  • 4. t-designs with t [actual symbol not reproducible] 3 / Gholamreza B. Khosrovshahi and Reinhard Laue
  • 5. Steiner systems / Charles J. Colbourn and Rudolf Mathon
  • 6. Symmetric designs / Yury J. Ionin and Tran Van Trung
  • 7. Resolvable and near-resolvable designs / R. Julian R. Abel, Gennian Ge and Jianxing Yin
  • III. Latin squares
  • 1. Latin squares / Charles J. Colbourn, Jeffrey H. Dinitz and Ian M. Wanless
  • 2. Quasigroups / Frank E. Bennett and Charles C. Lindner
  • 3. Mutually orthogonal latin squares (MOLS) / R. Julian R. Abel, Charles J. Colbourn and Jeffrey H. Dinitz
  • 4. Incomplete MOLS / R. Julian R. Abel, Charles J. Colbourn and Jeffrey H. Dinitz
  • 5. Self-orthogonal latin squares (SOLS) / Norman J. Finizio and L. Zhu
  • 6. Orthogonal arrays of index more than one / Malcolm Greig and Charles J. Colbourn
  • 7. Orthogonal arrays of strength more than two / Charles J. Colbourn
  • IV. Pairwise balanced designs
  • 1. PBDs and GDDs : the basics / Ronald C. Mullin and Hans-Dietrich O.F. Gronau
  • 2. PBDs : recursive constructions / Malcolm Greig and Ronald C. Mullin
  • 3. PBD-closure / R. Julian R. Abel, Frank E. Bennett and Malcolm Greig
  • 4. Group divisible designs / Gennian Ge
  • 5. PBDs, frames, and resolvability / Gennian Ge and Ying Miao
  • 6. Pairwise balanced designs as linear spaces / Anton Betten
  • V. Hadamard matrices and related designs
  • 1. Hadamard matrices and hadamard designs / Robert Craigen and Hadi Kharaghani
  • 2. Orthogonal designs / Robert Craigen and Hadi Kharaghani

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