An Introduction to Convex Polytopes

Released on by Arne Brondsted
preview-18

  • An Introduction to Convex Polytopes Book Detail

  • Author : Arne Brondsted
  • Release Date : 2012-12-06
  • Publisher : Springer Science & Business Media
  • Genre : Mathematics
  • Pages : 168
  • ISBN 13 : 1461211484
  • File Size : 91,91 MB
DOWNLOAD BOOK

An Introduction to Convex Polytopes by Arne Brondsted PDF Summary

Book Description: 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.

Disclaimer: www.yourbookbest.com does not own An Introduction to Convex Polytopes books pdf, neither created or scanned. We just provide the link that is already available on the internet, public domain and in Google Drive. If any way it violates the law or has any issues, then kindly mail us via contact us page to request the removal of the link.

An Introduction to Convex Polytopes

An Introduction to Convex Polytopes

File Size : 7,7 MB
Total View : 2951 Views
DOWNLOAD

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 combinat

Convex Polytopes

Convex Polytopes

File Size : 25,25 MB
Total View : 3629 Views
DOWNLOAD

"The original edition [...] inspired a whole generation of grateful workers in polytope theory. Without it, it is doubtful whether many of the subsequent advanc

Lectures on Polytopes

Lectures on Polytopes

File Size : 32,32 MB
Total View : 8946 Views
DOWNLOAD

Based on a graduate course at the Technische Universität, Berlin, these lectures present a wealth of material on the modern theory of convex polytopes. The str

Grobner Bases and Convex Polytopes

Grobner Bases and Convex Polytopes

File Size : 26,26 MB
Total View : 2672 Views
DOWNLOAD

This book is about the interplay of computational commutative algebra and the theory of convex polytopes. It centres around a special class of ideals in a polyn