图书信息
图书目录
差集：连接代数、组合与几何的桥梁 （影印版）
暂无简介
作者：
Emily H. Moore，Harriet S. Pollatsek 著
定价：
135.00 元
出版时间：
2026-03-27
ISBN：
978-7-04-065970-2
物料号：
65970-00
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
重点项目：
暂无
版面字数：
520.00千字
开本：
特殊
装帧形式：
精装
版次：
1
最新版次印刷时间：
2026-01-05
- 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
