An Introduction To Convex Polytopes PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download An Introduction To Convex Polytopes PDF full book. Access full book title An Introduction To Convex Polytopes.
Author | : Arne Brondsted |
Publisher | : Springer Science & Business Media |
Total Pages | : 168 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461211484 |
Download An Introduction to Convex Polytopes Book in PDF, ePub and Kindle
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.
Author | : Arne Brøndsted |
Publisher | : |
Total Pages | : 160 |
Release | : 1983-01 |
Genre | : Convex polytopes |
ISBN | : 9783540907220 |
Download An Introduction to Convex Polytopes Book in PDF, ePub and Kindle
Author | : P. McMullen |
Publisher | : CUP Archive |
Total Pages | : 196 |
Release | : 1971-07-02 |
Genre | : Mathematics |
ISBN | : 9780521080170 |
Download Convex Polytopes Book in PDF, ePub and Kindle
Author | : Günter M. Ziegler |
Publisher | : Springer |
Total Pages | : 388 |
Release | : 2012-05-03 |
Genre | : Mathematics |
ISBN | : 9780387943657 |
Download Lectures on Polytopes Book in PDF, ePub and Kindle
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 straightforward exposition features many illustrations, and complete proofs for most theorems. With only linear algebra as a prerequisite, it takes the reader quickly from the basics to topics of recent research. The lectures introduce basic facts about polytopes, with an emphasis on methods that yield the results, discuss important examples and elegant constructions, and show the excitement of current work in the field. They will provide interesting and enjoyable reading for researchers as well as students.
Author | : Bernd Sturmfels |
Publisher | : American Mathematical Soc. |
Total Pages | : 176 |
Release | : 1996 |
Genre | : Mathematics |
ISBN | : 0821804871 |
Download Grobner Bases and Convex Polytopes Book in PDF, ePub and Kindle
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 polynomial ring: the class of toric ideals. They are characterized as those prime ideals that are generated by monomial differences or as the defining ideals of toric varieties (not necessarily normal). The interdisciplinary nature of the study of Gröbner bases is reflected by the specific applications appearing in this book. These applications lie in the domains of integer programming and computational statistics. The mathematical tools presented in the volume are drawn from commutative algebra, combinatorics, and polyhedral geometry.
Author | : Günter M. Ziegler |
Publisher | : Springer Science & Business Media |
Total Pages | : 388 |
Release | : 2012-05-03 |
Genre | : Mathematics |
ISBN | : 038794365X |
Download Lectures on Polytopes Book in PDF, ePub and Kindle
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 straightforward exposition features many illustrations, and complete proofs for most theorems. With only linear algebra as a prerequisite, it takes the reader quickly from the basics to topics of recent research. The lectures introduce basic facts about polytopes, with an emphasis on methods that yield the results, discuss important examples and elegant constructions, and show the excitement of current work in the field. They will provide interesting and enjoyable reading for researchers as well as students.
Author | : Branko Grünbaum |
Publisher | : Springer Science & Business Media |
Total Pages | : 561 |
Release | : 2013-12-01 |
Genre | : Mathematics |
ISBN | : 1461300193 |
Download Convex Polytopes Book in PDF, ePub and Kindle
"The original edition [...] inspired a whole generation of grateful workers in polytope theory. Without it, it is doubtful whether many of the subsequent advances in the subject would have been made. The many seeds it sowed have since grown into healthy trees, with vigorous branches and luxuriant foliage. It is good to see it in print once again." --Peter McMullen, University College London
Author | : Anders Björner |
Publisher | : Cambridge University Press |
Total Pages | : 564 |
Release | : 1999-11-18 |
Genre | : Mathematics |
ISBN | : 052177750X |
Download Oriented Matroids Book in PDF, ePub and Kindle
First comprehensive, accessible account; second edition has expanded bibliography and a new appendix surveying recent research.
Author | : Jiri Matousek |
Publisher | : Springer Science & Business Media |
Total Pages | : 491 |
Release | : 2013-12-01 |
Genre | : Mathematics |
ISBN | : 1461300398 |
Download Lectures on Discrete Geometry Book in PDF, ePub and Kindle
The main topics in this introductory text to discrete geometry include basics on convex sets, convex polytopes and hyperplane arrangements, combinatorial complexity of geometric configurations, intersection patterns and transversals of convex sets, geometric Ramsey-type results, and embeddings of finite metric spaces into normed spaces. In each area, the text explains several key results and methods.
Author | : A.D. Alexandrov |
Publisher | : Springer Science & Business Media |
Total Pages | : 545 |
Release | : 2005-12-08 |
Genre | : Mathematics |
ISBN | : 3540263403 |
Download Convex Polyhedra Book in PDF, ePub and Kindle
This classic geometry text explores the theory of 3-dimensional convex polyhedra in a unique fashion, with exceptional detail. Vital and clearly written, the book includes the basics of convex polyhedra and collects the most general existence theorems for convex polyhedra that are proved by a new and unified method. This edition includes a comprehensive bibliography by V.A. Zalgaller, and related papers as supplements to the original text.