Symmetric Designs : An Algebraic Approach
Eric S. Lander
Bok Engelsk 1983 · Electronic books.
| Annen tittel | |
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| Utgitt | Cambridge , 1983
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| Omfang | 1 online resource (320 p.)
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| Opplysninger | Description based upon print version of record.. - 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. - 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.
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| Emner | |
| Sjanger | |
| Dewey | |
| ISBN | 052128693X
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