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

页数：

316

最新
印次时间：

2026年03月

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

目录
- 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