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设计理论2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载

Zhe-Xian Wan 著
出版社：北京：高等教育出版社
ISBN：9787040241648
出版时间：2009
标注页数：221页
文件大小：7MB
文件页数：231页
主题词：组合设计－理论研究－英文

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图书目录

1．BIBDs1

1.1 Definition and Fundamental Properties of BIBDs1

1.2 Isomorphisms and Automorphisms8

1.3 Constructions of New BIBDs from Old Ones12

1.4 Exercises14

2．Symmetric BIBDs15

2.1 Definition and Fundamental Properties15

2.2 Bruck-Ryser-Chowla Theorem21

2.3 Finite Projective Planes as Symmetric BIBDs26

2.4 Difference Sets and Symmetric BIBDs30

2.5 Hadamard Matrices and Symmetric BIBDs43

2.6 Derived and Residual BIBDs51

2.7 Exercises52

3．Resolvable BIBDs55

3.1 Definitions and Examples55

3.2 Finite Affine Planes57

3.3 Properties of Resolvable BIBDs61

3.4 Exercises67

4．Orthogonal Latin Squares69

4.1 Orthogonal Latin Squares69

4.2 Mutually Orthogonal Latin Squares74

4.3 Singular Direct Product of Latin Squares79

4.4 Sum Composition of Latin Squares84

4.5 Orthogonal Arrays89

4.6 Transversal Designs92

4.7 Exercises95

5．Pairwise Balanced Designs;Group Divisible Designs97

5.1 Pairwise Balanced Designs97

5.2 Group Divisible Designs106

5.3 Closedness of Some Sets of Positive Integers111

5.4 Exercises115

6．Construction of Some Families of BIBDs117

6.1 Steiner Triple Systems117

6.2 Cyclic Steiner Triple Systems123

6.3 Kirkman Triple Systems131

6.4 Triple Systems142

6.5 Biplanes147

6.6 Exercises153

7．t-Designs155

7.1 Definition and Fundamental Properties of t-Designs155

7.2 Restriction and Extension162

7.3 Extendable SBIBDs and Hadamard 3-Designs166

7.4 Finite Inversive Planes173

7.5 Exercises176

8．Steiner Systems177

8.1 Steiner Systems177

8.2 Some Designs from Hadamard 2-Designs and 3-Designs179

8.3 Steiner Systems S(4;11,5)and S(5;12,6)185

8.4 Binary Codes191

8.5 Binary Golay Codes and Steiner Systems S(4;23,7)and S(5;24,8)196

8.6 Exercises200

9．Association Schemes and PBIBDs201

9.1 Association Schemes201

9.2 PBIBDs206

9.3 Association Schemes(Continued)207

9.4 Exercises216

References217