凸圆体与离散几何学 CTM:The Cube-A Window to Convex and Discrete Geometry (Cambridge Tracts in Mathematics)
分類: 图书,进口原版书,科学与技术 Science & Techology ,
作者: Chuanming Zong著
出 版 社: Oversea Publishing House
出版时间: 2006-9-1字数:版次: 1页数: 174印刷时间: 2006/09/01开本: 16开印次: 1纸张: 胶版纸I S B N : 9780521855358包装: 精装内容简介
Eight topics about the unit cubes are introduced within this textbook: cross sections, projections, inscribed simplices, triangulations, 0/1 polytopes, Minkowski's conjecture, Furtwangler's conjecture, and Keller's conjecture. In particular Chuanming Zong demonstrates how deep analysis like log concave measure and the Brascamp-Lieb inequality can deal with the cross section problem, how Hyperbolic Geometry helps with the triangulation problem, how group rings can deal with Minkowski's conjecture and Furtwangler's conjecture, and how Graph Theory handles Keller's conjecture.
目录
Preface
Basic notation
Introduction
1 Cross sections
1.1 Introduction
1.2 Good's conjecture
1.3 Hensley's conjecture
1.4 Additional remarks
2 Projections
2.1 Introduction
2.2 Lower bounds and upper bounds
2.3 A symmetric formula
2.4 Combinatorial shapes
3 Inscribed simplices
3.1 Introduction
3.2 Binary matrices
3.3 Upper bounds
3.4 Some particular cases
4 Triangulations
4.1 An example
4.2 Some special triangulations
4.3 Smith's lower bound
4.4 Lower-dimensional cases
5 0/1 polytopes
5.1 Introduction
5.2 0/1 polytopes and coding theory
5.3 Classification
5.4 The number of facets
6 Minkowski's conjecture
6.1 Minkowski's conjecture
6.2 An algebraic version
6.3 Haj6s' proof
6.4 Other versions
7 Furtwaingler's conjecture
7.1 Furtwaingler's conjecture
7.2 A theorem of Furtwaingler and Haj6s
7.3 Haj6s' counterexamples
7.4 Robinson's characterization
8 Keller's conjecture
8.1 Keller's conjecture
8.2 A theorem of Keller and Perron
8.3 Corradi and Szab6's criterion
8.4 Lagarias, Mackey, and Shor's counterexamples
References
Index