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Symmetric designs : an algebraic approach /
Symmetric designs are an important class of combinatorial structures which arose first in the statistics and are now especially important in the study of finite geometries. This book presents some of the algebraic techniques that have been brought to bear on the question of existence, construction a...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge [Cambridgeshire] ; New York :
Cambridge University Press,
1983.
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| Colección: | London Mathematical Society lecture note series ;
74. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Cover; Title; Copyright; Dedication; Contents; Preface; CHAPTER 1. SYMMETRIC DESIGNS; 1.1 Definitions and simple examples; 1.2 Hadamard matrices and designs; 1.3 Projective geometries; 1.4 t-designs; 1.5 Dembowski-Wagner Theorem; Problems; Supplementary Problems: Algebraic geometry; Notes; CHAPTER 2. AN ALGEBRAIC APPROACH; 2.1 Existence criteria; 2.2 The code of a symmetric design; 2.3 The module of a symmetric design; Problems; Notes; CHAPTER 3. AUTOMORPHISMS; 3.1 Fixed points and blocks; 3.2 Doubly-transitive symmetric designs; 3.3 Automorphisms of prime order
- 3.4 Counting orbitsProblems; Supplementary Problems: Eigenvalue techniques; Notes; CHAPTER 4. DIFFERENCE SETS; 4.1 Introduction and examples; 4.2 Abelian difference sets; 4.3 Contracting difference sets; 4.4 G-matrices; 4.5 Difference sets with multiplier -1; 4.6 Cyclic groups are special; 4.7 More on cyclic groups; 4.8 Further results; Problems; Notes; CHAPTER 5. MULTIPLIER THEOREMS; 5.1 The automorphism theorem; 5.2 Contracted automorphism theorem; 5.3 Blocks fixed by multipliers; 5.4 Further multiplier theorems; 5.5 Still further multiplier theorems; Problems; Notes
- CHAPTER 6. OPEN QUESTIONS6.1 Existence; 6.2 Cyclic Sylow subgroups; 6.3 Cyclic projective planes; 6.4 Multiplier theorems; 6.5 Tables; APPENDIX; A. Permutation Groups; B. Bilinear and Quadratic Forms; C. Invariant Factors; D. Representation Theory; E. Cyclotomic Fields; F. P-adic Numbers; REFERENCES; INDEX