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矩阵结合方案 英文版【2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载】

矩阵结合方案 英文版
  • 王仰贤等著 著
  • 出版社： 北京：外文出版社
  • ISBN：9787030266163
  • 出版时间：2010
  • 标注页数：235页
  • 文件大小：7MB
  • 文件页数：247页
  • 主题词：矩阵－结合方案－英文

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图书目录

Chapter 1 Basic Theory of Association Schemes1

1.1 Definition of Association Scheme1

1.2 Examples4

1.3 The Eigenvalues of Association Schemes7

1.4 The Krein Parameters12

1.5 S-Rings and Duality16

1.6 Primitivity and Imprimitivity20

1.7 Subschemes and Quotient Schemes25

1.8 The Polynomial Property29

1.9 The Automorphisms34

Chapter 2 Association Schemes of Rectangular Matrices36

2.1 Definition and Primitivity36

2.2 The Polynomial Property of Association Schemes of Rectangular Matrices39

2.3 Recurrence Formulas for Intersection Numbers42

2.4 The Duality of Association Schemes of Rectangular Matrices48

2.5 The Automorphisms of Mat(m×n,q)50

Chapter 3 Association Schemes of Alternate Matrices52

3.1 Primitivity and P-polynomial Property52

3.2 The Parameters of Γ（1）54

3.3 Recurrences for Intersection Numbers58

3.4 Recurrences for Intersection Numbers:Continued62

3.5 The Self-duality of Alt(n,q)66

3.6 The Automorphisms of Alt(n,q)67

Chapter 4 Association Schemes of Hermitian Matrices69

4.1 Primitivity and P-polynomial Property69

4.2 The Parameters of Graph Г（1）71

4.3 Recurrences for Intersection Numbers74

4.4 Recurrences for Intersection Numbers:Continued77

4.5 The Self-duality of Her(n,q2)80

4.6 The Automorphisms of Her(n,q2)81

Chapter 5 Association Schemes of Symmetric Matrices in Odd Characteristic82

5.1 The Normal Forms of Symmetric Matrices82

5.2 The Association Schemes of Symmetric Matrices and Their Primitivity83

5.3 Sym(n,q)for Small n87

5.4 A Few Enumeration Formulas from Orthogonal Geometry92

5.5 Calculation of Intersection Numbers96

5.6 Calculation of Intersection Numbers:Continued101

5.7 The Association Scheme Quad(n,q)109

5.8 The Self-duality of Sym(n,q)121

5.9 The Automorphisms of Sym(n,q)122

Chapter 6 Association Schemes of Symmetric Matrices in Even Characteristic128

6.1 The Normal Forms of Symmetric Matrices128

6.2 The Imprimitivity of Sym(n,q)129

6.3 The Association Scheme Sym(2,q)130

6.4 Some Results of Pseudo-symplectic Geometry135

6.5 Calculation of Intersection Numbers138

6.6 Calculation of Intersection Numbers:Continued145

6.7 A Fusion Scheme of Sym(n,q)150

6.8 The Automorphisms of Sym(n,q)154

Chapter 7 Association Schemes of Quadratic Forms in Even Characteristic156

7.1 The Normal Forms of Quadratic Forms156

7.2 Qua(2,q)and Qua(3,q)160

7.3 Some Enumeration Formulas from Orthogonal Geometry166

7.4 Calculation of Intersection Numbers172

7.5 The Duality of Association Schemes of Quadratic Forms186

7.6 The Imprimitivity of Association Schemes of Quadratic Forms190

7.7 Two Fusion Schemes of Qua(n,q)192

7.8 The Automorphisms of Association Schemes of Quadratic Forms199

Chapter 8 The Eigenvalues of Association Schemes of Quadratic Forms207

8.1 The Eigenvalues of Association Scheme Qua(2,q)207

8.2 Some Lemmas on Additive Characters209

8.3 The 1-extensions and f(n)r211

8.4 Values of f(n)r on the Union Classes C(n)2i215

8.5 The 2-extensions and f(n)2k218

8.6 Values of f(n)2k on Classes C(n)2i and C(n)2i ∪C(n)2i-1227

8.7 Dual Schemes of Two Fusion Schemes of Qua(n,q)229

8.8 Eigenvalues of Small Association Schemes of Quadratic Forms230

References233

Index235

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