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Cube-A Window to Convex and Discrete Geometry

ISBN-10: 0521855357

ISBN-13: 9780521855358

Edition: 2005

Authors: Chuanming Zong, B. Bollobas, W. Fulton, A. Katok, F. Kirwan

List price: $129.99
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Description:

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.
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Book details

List price: $129.99
Copyright year: 2005
Publisher: Cambridge University Press
Publication date: 2/2/2006
Binding: Hardcover
Pages: 184
Size: 6.00" wide x 9.25" long x 0.75" tall
Weight: 0.836
Language: English

Preface
Basic notation
Introduction
Cross sections
Introduction
Good's conjecture
Hensley's conjecture
Additional remarks
Projections
Introduction
Lower bounds and upper bounds
A symmetric formula
Combinatorial shapes
Inscribed simplices
Introduction
Binary matrices
Upper bounds
Some particular cases
Triangulations
An example
Some special triangulations
Smith's lower bound
Lower-dimensional cases
0/1 polytopes
Introduction
0/1 polytopes and coding theory
Classification
The number of facets
Minkowski's conjecture
Minkowski's conjecture
An algebraic version
Hajos' proof
Other versions
Furtwangler's conjecture
Furtwangler's conjecture
A theorem of Furtwangler and Hajos
Hajos' counterexamples
Robinson's characterization
Keller's conjecture
Keller's conjecture
A theorem of Keller and Perron
Corradi and Szabo's criterion
Lagarias, Mackey, and Shor's counterexamples
References
Index