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An Introduction to Convex Polytopes by Arne Brondsted (Hardcover, 1982)

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The aim of this book is to introduce the reader to the fascinating world of convex polytopes. All the background information on convex sets and convex polytopes which is m~eded to under stand and appreciate these three theorems is developed in detail.

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The aim of this book is to introduce the reader to the fascinating world of convex polytopes. The highlights of the book are three main theorems in the combinatorial theory of convex polytopes, known as the Dehn-Sommerville Relations, the Upper Bound Theorem and the Lower Bound Theorem. All the background information on convex sets and convex polytopes which is m~eded to under stand and appreciate these three theorems is developed in detail. This background material also forms a basis for studying other aspects of polytope theory. The Dehn-Sommerville Relations are classical, whereas the proofs of the Upper Bound Theorem and the Lower Bound Theorem are of more recent date: they were found in the early 1970's by P. McMullen and D. Barnette, respectively. A famous conjecture of P. McMullen on the charac terization off-vectors of simplicial or simple polytopes dates from the same period; the book ends with a brief discussion of this conjecture and some of its relations to the Dehn-Sommerville Relations, the Upper Bound Theorem and the Lower Bound Theorem. However, the recent proofs that McMullen's conditions are both sufficient (L. J. Billera and C. W. Lee, 1980) and necessary (R. P. Stanley, 1980) go beyond the scope of the book. Prerequisites for reading the book are modest: standard linear algebra and elementary point set topology in [R1d will suffice.

Product Identifiers

Publisher
Springer-Verlag New York Inc.
ISBN-13
9780387907222
eBay Product ID (ePID)
94492201

Product Key Features

Number of Pages
162 Pages
Language
English
Publication Name
An Introduction to Convex Polytopes
Publication Year
1982
Subject
Mathematics
Type
Textbook
Author
Arne Brondsted
Format
Hardcover

Dimensions

Item Height
235 mm
Item Weight
940 g
Item Width
155 mm
Volume
90

Additional Product Features

Country/Region of Manufacture
United States
Title_Author
Arne Brondsted
Series Title
Graduate Texts in Mathematics
LeafCats
378

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item 1 Introduction to Convex Polytopes, Hardcover by Bronsted, Arne...
AU $17.50
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item 2 Introduction to Convex Polytopes, Hardcover by Bronsted, Arne...
AU $45.00
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An Introduction to Convex Polytopes by Arne Brondsted (Hardcover, 1982)

About this product

Product Information

Product Identifiers

Product Key Features

Dimensions

Additional Product Features

All listings for this product

item 1 Introduction to Convex Polytopes, Hardcover by Bronsted, Arne...

item 2 Introduction to Convex Polytopes, Hardcover by Bronsted, Arne...

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