Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Convex Polytopes PDF full book. Access full book title Convex Polytopes by Branko Grünbaum. Download full books in PDF and EPUB format.
Author: Branko Grünbaum Publisher: Springer Science & Business Media ISBN: 1461300193 Category : Mathematics Languages : en Pages : 561
Book Description
"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: Branko Grünbaum Publisher: Springer Science & Business Media ISBN: 1461300193 Category : Mathematics Languages : en Pages : 561
Book Description
"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: Arne Brondsted Publisher: Springer Science & Business Media ISBN: 1461211484 Category : Mathematics Languages : en Pages : 168
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.
Author: Bernd Sturmfels Publisher: American Mathematical Soc. ISBN: 0821804871 Category : Mathematics Languages : en Pages : 176
Book Description
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 ISBN: 038794365X Category : Mathematics Languages : en Pages : 388
Book Description
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: Günter M. Ziegler Publisher: Springer ISBN: 9780387943657 Category : Mathematics Languages : en Pages : 388
Book Description
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: Gil Kalai Publisher: Birkhäuser ISBN: 3034884389 Category : Mathematics Languages : en Pages : 228
Book Description
Questions that arose from linear programming and combinatorial optimization have been a driving force for modern polytope theory, such as the diameter questions motivated by the desire to understand the complexity of the simplex algorithm, or the need to study facets for use in cutting plane procedures. In addition, algorithms now provide the means to computationally study polytopes, to compute their parameters such as flag vectors, graphs and volumes, and to construct examples of large complexity. The papers of this volume thus display a wide panorama of connections of polytope theory with other fields. Areas such as discrete and computational geometry, linear and combinatorial optimization, and scientific computing have contributed a combination of questions, ideas, results, algorithms and, finally, computer programs.
Author: Jürgen Richter-Gebert Publisher: Springer ISBN: 3540496408 Category : Mathematics Languages : en Pages : 195
Book Description
The book collects results about realization spaces of polytopes. It gives a presentation of the author's "Universality Theorem for 4-polytopes". It is a comprehensive survey of the important results that have been obtained in that direction. The approaches chosen are direct and very geometric in nature. The book is addressed to researchers and to graduate students. The former will find a comprehensive source for the above mentioned results. The latter will find a readable introduction to the field. The reader is assumed to be familiar with basic concepts of linear algebra.
Author: A.D. Alexandrov Publisher: Springer Science & Business Media ISBN: 3540263403 Category : Mathematics Languages : en Pages : 545
Book Description
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.
Author: Branko Grünbaum
Author: Branko Grünbaum
Author: Arne Brondsted
Author: Bernd Sturmfels
Author: P. McMullen
Author: Günter M. Ziegler
Author: Günter M. Ziegler
Author: Gil Kalai
Author: Jürgen Richter-Gebert
Author: Anders Björner
Author: A.D. Alexandrov