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Lectures on polytopes / Günter M. Ziegler.
Author
Ziegler, Günter M.
[Browse]
Format
Book
Language
English
Published/Created
New York : Springer-Verlag, ©1995.
Description
ix, 370 pages : illustrations ; 24 cm.
Availability
Copies in the Library
Location
Call Number
Status
Location Service
Notes
Lewis Library - Stacks
QA691 .Z54 1995
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Details
Subject(s)
Polytopes
[Browse]
Series
Graduate texts in mathematics ; 152.
[More in this series]
Summary note
Based on a graduate course given at the Technische Universitat Berlin, these lectures present a wealth of material on the modern theory on convex polytopes. the clear and straightforward presentation features many illustrations, a provides complete proofs for most theorems. The material requires only linear algebra as a pre-requisite, but takes the reader quickly from the basics to topics of recent research, including a number of unanswered questions.
The lectures introduce the basic facts about polytypes, with an emphasis on the methods that yield the results (Fourier-Motzkin elimination, Schelegel diagrams, shellability, Gale diagrams, and oriented matroids), discuss important examples and elegant constructions (cyclic and neighborly polytopes, zonotopes, Minkowski sums, permatathedra and associhedra, fiber polytopes, and Lawrence construction), and show the excitement of current work in the field (Kalai's new diameter bounds, construction of non-radial polytopes, the Bohne-Dresstiling theorem, the upper bound theorem, and nonextendable shellings). They should provide interesting and enjoyable reading for researchers as well as students. -- back cover
Bibliographic references
Includes bibliographical references (p. [325]-363) and index.
Contents
1. Polytopes, Polyhedra, and Cones
2. Faces of Polytopes
3. Graphs of Polytopes
4. Steinitz' Theorem for 3-Polytopes
5. Schlegel Diagrams for 4-Polytopes
6. Duality, Gale Diagrams, and Applications
7. Fans, Arrangements, Zonotopes, and Tilings
8. Shellability and the Upper Bound Theorem
9. Fiber Polytopes, and Beyond.
Show 6 more Contents items
ISBN
0387943293 ((New York ; : hard cover))
9780387943299 ((New York ; : hard cover))
3540943293 ((Berlin ; : hard cover))
9783540943297 ((Berlin ; : hard cover))
038794365X ((New York ; : softcover))
9780387943657 ((New York ; : softcover))
354094365X ((Berlin ; : softcover))
9783540943655 ((Berlin ; : softcover))
LCCN
94021784
OCLC
30594158
Other standard number
99819472389
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