Design Theory:

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Cambridge University Press, Nov 18, 1999 - Mathematics - 1100 pages
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This volume concludes the second edition of the standard text on design theory. Since the first edition there has been extensive development of the theory and this book has been thoroughly rewritten to reflect this. In particular, the growing importance of discrete mathematics to many parts of engineering and science have made designs a useful tool for applications, a fact that has been acknowledged here with the inclusion of an additional chapter on applications. The volume is suitable for advanced courses and for reference use, not only for researchers in discrete mathematics or finite algebra, but also for those working in computer and communications engineering and other mathematically oriented disciplines. Features include exercises and an extensive, updated bibliography of well over 1800 citations.
  

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Contents

Recursive constructions
608
Difference families 468
611
2 Use of pairwise balanced designs
617
3 Applications of divisible designs
621
4 Applications of Hananis lemmas
627
5 Block designs of block size three and four
636
6 Solution of Kirkmans schoolgirl problem
641
7 The basis of a closed set
644
6 The main theorem for A 1
796
7 An existence theorem for resolvable block designs
801
8 Some results for t 3
805
Characterisations of classical designs
806
2 Characterisations of projective spaces
808
3 Characterisation of affine spaces
821
4 Locally projective linear spaces
828
5 Good blocks
833

8 Block designs with block size five
651
Further direct constructions 520
653
9 Divisible designs with small block sizes
660
10 Steiner quadruple systems
664
11 Embedding theorems for designs and partial designs
673
12 Concluding remarks
681
Transversal designs and nets
690
2 Transversal designs with A 1
693
3 A construction of Wilson
696
4 Six and more mutually orthogonal Latin squares
703
5 The theorem of Chowla Erdos and Straus
706
6 Further bounds for transversal designs and orthogonal arrays
708
7 Completion theorems for Bruck nets
713
8 Maximal nets with large deficiency
725
9 Translation nets and maximal nets with small deficiency
731
Examples and basic definitions 1
737
3 designs Steiner systems and configurations 15
738
10 Completion results for fj 1
749
11 Extending symmetric nets
758
12 Complete mappings difference matrices and maximal nets
761
13 Tarrys theorem
772
14 Codes of Bruck nets
778
Asymptotic existence theory
781
2 The existence of Steiner systems with u in given residue classes
783
3 The main theorem for Steiner systems S2 k v
787
4 The eventual periodicity of closed sets
790
5 The main theorem for A 1
793
6 Concluding remarks
841
Applications of designs
852
2 Design of experiments
856
3 Experiments with Latin squares and orthogonal arrays
874
4 Application of designs in optics
880
5 Codes and designs
892
6 Discrete tomography
926
7 Designs in data structures and computer algorithms
930
8 Designs in hardware
937
9 Difference sets rule matter and waves
946
10 No waves no rules but security
956
Appendix Tables
971
2 Symmetric designs
981
Notation and symbols
1005
Bibliography
1013
Combinatorial analysis of designs 62
1025
Witt designs and Mathieu groups 234
1029
Highly transitive groups 277
1037
4 The BruckRyserChowla theorem 89
1045
7 Extensions of designs
1051
8 Affine designs 123
1055
9 Strongly regular graphs 136
1064
10 The HallConnor theorem 146
1067
Difference sets and regular symmetric designs 297
1091
Index
1093
Copyright

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About the author (1999)

Jungnickel of the University of Augsburg, Germany

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