An Introduction to Convex Polytopes - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook An Introduction to Convex Polytopes write by Arne Brondsted. This book was released on 2012-12-06. An Introduction to Convex Polytopes available 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.
An Introduction to Convex Polytopes
An Introduction to Convex Polytopes - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook An Introduction to Convex Polytopes write by Arne Brøndsted. This book was released on 1983-01. An Introduction to Convex Polytopes available in PDF, EPUB and Kindle.
Convex Polytopes
Convex Polytopes - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Convex Polytopes write by Branko Grünbaum. This book was released on 2013-12-01. Convex Polytopes available 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
Grobner Bases and Convex Polytopes
Grobner Bases and Convex Polytopes - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Grobner Bases and Convex Polytopes write by Bernd Sturmfels. This book was released on 1996. Grobner Bases and Convex Polytopes available 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.
Lectures on Polytopes
Lectures on Polytopes - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Lectures on Polytopes write by Günter M. Ziegler. This book was released on 2012-05-03. Lectures on Polytopes available 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.
