Design Theory: Volume 2This 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. |
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 |
Applications of designs | 852 |
4 Application of designs in optics | 880 |
Groups and designs | 892 |
32 | 919 |
5 Codes and designs | 920 |
6 Discrete tomography | 926 |
8 Designs in hardware | 937 |
9 Difference sets rule matter and waves | 946 |
8 Block designs with block size five | 651 |
9 Divisible designs with small block sizes | 660 |
10 Steiner quadruple systems | 664 |
3 tdesigns Steiner systems and configurations 4 Isomorphisms duality and correlations 5 Partitions of the block set and resolvability 6 Divisible incide... | 668 |
11 Embedding theorems for designs and partial designs | 673 |
12 Concluding remarks | 681 |
Transversal designs and nets | 690 |
2 Transversal designs with λ 1 | 693 |
3 A construction of Wilson | 696 |
4 Six and more mutually orthogonal Latin squares | 703 |
5 The theorem of Chowla Erdös 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 |
7 Transversal designs and nets | 758 |
12 Complete mappings difference matrices and maximal nets | 761 |
13 Tarrys theorem | 778 |
3 The main theorem for Steiner systems S2 k | 787 |
5 The main theorem for λ 1 | 793 |
7 An existence theorem for resolvable block designs | 801 |
8 Subspaces 1 6 | 831 |
15 | 838 |
20 | 840 |
24 | 844 |
10 No waves no rules but security | 956 |
Appendix Tables | 971 |
50 | 974 |
64 | 975 |
96 | 976 |
123 | 977 |
136 | 978 |
152 | 979 |
2 Fishers inequality for pairwise balanced designs 3 Symmetric designs | 989 |
4 The BruckRyserChowla theorem | 993 |
Further direct constructions 520 | 1001 |
Notation and symbols | 1005 |
5 Balanced incidence structures with balanced duals 6 Generalisations of Fishers inequality and intersection numbers | 1011 |
| 1013 | |
| 1017 | |
9 Strongly regular graphs | 1024 |
Highly transitive groups | 1037 |
| 1051 | |
| 1059 | |
| 1067 | |
| 1068 | |
| 1075 | |
| 1093 | |
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Common terms and phrases
2-design abelian affine design affine plane algebra algorithms applications assertion assume automorphism group Beth block designs Bose characterisation codeword coding theory Colbourn and Dinitz Comb combinatorial consider construction contains Corollary corresponding cosets cyclic decoding defined Definition Delandtsheer denote design theory difference sets Discr disjoint equation error exactly example existence Figure finite following result generalised geometry GF(q given graph Hadamard designs Hadamard matrices Hadamard transform Hamming code Hanani Hence implies incidence matrix incidence structure intersect isomorphic Jungnickel Lemma linear spaces lines Math Mathon matrix necessary conditions notation obtained orthogonal Latin squares parallel class parameters permutation point classes point set positive integer prime power problem projective plane projective space Proof Proposition proved Remark Rosa Section sequence Series Shrikhande Steiner systems Steiner triple systems subset subspace symmetric design Table TD[k Theorem transversal designs triple systems unique vector
Popular passages
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