Design Theory / D.R. Hughes, F. Piper.
Design theory has grown to be a subject of considerable interest in mathematics, not only in itself, but for its connections to other fields such as geometry, group theory, graph theory and coding theory. This textbook, first published in 1985, is intended to be an accessible introduction to the sub...
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| Other title: | Cambridge books online. |
| Format: | Electronic eBook |
| Language: | English |
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Cambridge :
Cambridge University Press,
1985.
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Table of Contents:
- Cover; Half-title; Title; Copyright; Contents; Introduction; 1 Basic concepts ; 1.1 Introduction ; 1.2 Basic definitions and properties ; 1.3 Examples ; 1.4 Related structures ; 1.5 The incidence matrix ; 1.6 Block's Lemma and the Orbit Theorem ; 1.7 Graphs ; References; 2 Symmetric designs ; 2.1 Introduction.
- 2.2 Residual structures 2.3 The Bruck-Ryser-Chowla Theorem ; 2.4 Singer groups and difference sets ; 2.5 Multipliers ; 2.6 Arithmetical relations and Hadamard 2-desigps ; 2.7 The Dembowski-Wagner Theorem ; References; 3 Some families of symmetric designs; 3.1 Introduction ; 3.2 Projective and affine planes.
- 3.3 Latin squares 3.4 Nets ; 3.5 Hadamard matrices and Hadamard 2-designs ; 3.6 Biplanes ; 3.7 Strongly regular graphs ; References; 4 3-Designs and related topics ; 4.1 Introduction ; 4.2 Cameron's Theorem and Hadamard 3-design^ ; 4.3 Inversive planes and a class of 3-designs.
- 4.4 Hadamard designs, the little Mathieu designs and the little Mathieu groups 4.5 Some 4-designs and 5-designs ; 4.6 Tight designs ; References; 5 Resolutions ; 5.1 Introduction ; 5.2 Resolutions ; 5.3 Strong resolutions ; 5.4 Strongly resolvable designs.
- 5.5 Examples of strongly resolvable designs References; 6 Other 2-designs ; 6.1 Introduction ; 6.2 Steiner triple systems ; 6.3 Unitals ; 6.4 Groups and more 2-designs ; References; 7 Some 1-designs ; 7.1 Introduction ; 7.2 Semilinear spaces and Ta-geometries ; 7.3 Generalised quadrangles.