9783540907220
An Introduction To Convex Polytopes - Arne Brøndsted
Springer-Verlag (1983)
In Collection
#7950

Read It:
Yes
Convex Polytopes

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 needed to understand and appreciate these three theorems is developed in detail. This background material also forms a basis for studying other aspects ofpolytope 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 characterization 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 will suffice. The author is grateful to the many people who have contributed to the book: several colleagues, in particular Victor Klee and Erik Sparre Andersen, supplied valuable information; Aage Bondesen suggested essential improvements; students at the University of Copenhagen also suggested improvements; and Ulla Jacobsen performed an excellent typing j

Product Details
LoC Classification QA640.3 .B76 1982
Dewey 514/.223
No. of Pages 160
Height x Width 250 x 159 mm