Cube-A Window to Convex and Discrete Geometry

Name: Cube-A Window to Convex and Discrete Geometry
Price: 69.73 USD
Availability: InStock
ISBN: 9780521855358

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.

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