差集：连接代数、组合与几何的桥梁（影印版）

样章

作者：

Emily H. Moore，Harriet S. Pollatsek 著

定价：

135.00元

版面字数：

520.00千字

开本：

特殊

装帧形式：

精装

版次：

最新版次
印刷时间：

2026-01-05

ISBN：

978-7-04-065970-2

物料号：

65970-00

出版时间：

2026-03-27

读者对象：

学术著作

一级分类：

自然科学

二级分类：

数学与统计

三级分类：

组合数学与图论

暂无

前辅文
Preface
Chapter 1. Introduction
Chapter 2. Designs
- 2.1. Incidence structures
- 2.2. t-Designs
- 2.3. Affine planes
- 2.4. Symmetric designs
- 2.5. Projective geometry
Chapter 3. Automorphisms of Designs
- 3.1. Group actions
- 3.2. Automorphisms of symmetric designs
Chapter 4. Introducing Difference Sets
- 4.1. Definition and examples
- 4.2. Difference sets and designs
- 4.3. Integral group ring
- 4.4. Equivalence
Chapter 5. Bruck-Ryser-Chowla Theorem
- 5.1. The BRC Theorem
- 5.2. Proof of BRC for v odd
- 5.3. Partial converse and extension of BRC
Chapter 6. Multipliers
- 6.1. Definition and examples
- 6.2. Existence of numerical multipliers
- 6.3. Multipliers fix sD
- 6.4. Using multipliers
- 6.5. Multipliers in non-cyclic groups
Chapter 7. Necessary Group Conditions
- 7.1. Intersection numbers
- 7.2. Turyn’s exponent bound
- 7.3. Dillon’s dihedral trick
Chapter 8. Difference Sets from Geometry
- 8.1. Singer difference sets
- 8.2. Turyn’s construction
- 8.3. McFarland difference sets
Chapter 9. Families from Hadamard Matrices
- 9.1. Hadamard matrices
- 9.2. Paley-Hadamard family: v=4n−1
- 9.3. Hadamard family: v=4n
Chapter 10. Representation Theory
- 10.1. Definitions and examples
- 10.2. Equivalent representations
- 10.3. Maschke’s Theorem
- 10.4. Representations and difference sets
Chapter 11. Group Characters
- 11.1. Definitions and examples
- 11.2. The Fundamental Theorem
- 11.3. Proof of the Fundamental Theorem
- 11.4. Characters and difference sets
- 11.5. Character tables
Chapter 12. Using Algebraic Number Theory
- 12.1. Why algebraic number theory?
- 12.2. Definitions and basic facts
- 12.3. Seeking difference sets
- 12.4. Proving Turyn’s exponent bound
Chapter 13. Applications
- 13.1. Binary sequences
- 13.2. Imaging with coded masks
- 13.3. Error correcting codes
- 13.4. Quantum information and MUBs
Appendix A. Background
Appendix B. Notation
Appendix C. Hints and Solutions to Selected Exercises
Bibliography
Index
Index of Parameters