This volume consists of research papers and expository survey articles presented by the invited speakers of the Summer Workshop on Lattice Polytopes. Topics include enumerative, algebraic and geometric combinatorics on lattice polytopes, topological combinatorics, commutative algebra and toric varieties.
Readers will find that this volume showcases current trends on lattice polytopes and stimulates further developments of many research areas surrounding this field. With the survey articles, research papers and open problems, this volume provides its fundamental materials for graduate students to learn and researchers to find exciting activities and avenues for further exploration on lattice polytopes.
Автор: GrГјnbaum Branko, Ziegler GГјnter M. Название: Convex polytopes / second edition ISBN: 0387004246 ISBN-13(EAN): 9780387004242 Издательство: Springer Рейтинг: Цена: 11878.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The appearance of Gruenbaum's book Convex Polytopes in 1967 was a moment of grace to geometers and combinatorialists. The special spirit of the book is very much alive even in those chapters where the book's immense influence made them quickly obsolete. Some other chapters promise beautiful unexplored land for future research. The appearance of the new edition is going to be another moment of grace. Kaibel, Klee and Ziegler were able to update the convex polytope saga in a clear, accurate, lively, and inspired way. --Gil Kalai, The Hebrew University of Jerusalem The original book of Gruenbaum has provided the central reference for work in this active area of mathematics for the past 35 years...I first consulted this book as a graduate student in 1967; yet, even today, I am surprised again and again by what I find there. It is an amazingly complete reference for work on this subject up to that time and continues to be a major influence on research to this day. --Louis J. Billera, Cornell University The original edition of Convex Polytopes 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
Автор: Ziegler GГјnter M. Название: Lectures on polytopes ISBN: 038794365X ISBN-13(EAN): 9780387943657 Издательство: Springer Рейтинг: Цена: 5304.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Based on a graduate course given at the Technische UniversitГ¤t, Berlin, these lectures present a wealth of material on the modern theory of convex polytopes. The clear and straightforward presentation features many illustrations, and provides complete proofs for most theorems. The material requires only linear algebra as a prerequisite, but takes the reader quickly from the basics to topics of recent research, including a number of unanswered questions. The lectures - introduce the basic facts about polytopes, with an emphasis on the methods that yield the results (Fourier-Motzkin elimination, Schlegel diagrams, shellability, Gale transforms, and oriented matroids) - discuss important examples and elegant constructions (cyclic and neighborly polytopes, zonotopes, Minkowski sums, permutahedra and associhedra, fiber polytopes, and the Lawrence construction) - show the excitement of current work in the field (Kalai's new diameter bounds, construction of non-rational polytopes, the Bohne-Dress tiling theorem, the upper-bound theorem), and nonextendable shellings) They should provide interesting and enjoyable reading for researchers as well as students.
Автор: J?rgen Richter-Gebert Название: Realization Spaces of Polytopes ISBN: 3540620842 ISBN-13(EAN): 9783540620846 Издательство: Springer Рейтинг: Цена: 4186.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This text collects the results about realization spaces of polytopes. It gives a presentation of the author`s theorem for 4-polytopes. It is a comprehesive survey of the results that have been obtained in this area of study.
Автор: Kalai, Gil; Ziegler, Gunter M. (Eds.) Название: Polytopes - combinatorics and computation ISBN: 3764363517 ISBN-13(EAN): 9783764363512 Издательство: Springer Рейтинг: Цена: 4884.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: 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.
Описание: This book contains a meticulous geometric investigation of the 5 Platonic Solids and 5 other important polyhedra, as well as reference charts for each solid. It also has a geometric explanation of the Phi Ratio and Fibonacci series, and a detailed analysis of the pentagon, which forms the basis for many of these solids.
Описание: Getting Inside the Mind of Nature Discover the simple but powerful mathematics of the underlying geometric figures that shape our world
Can geometry be exciting?
It can for those who can appreciate the beauty of numbers and their relationships.
This book contains a meticulous geometric investigation of the 5 Platonic Solids and 5 other important polyhedra, as well as reference charts for each solid.
Poly (many) hedron (face) means "many faces." Polyhedra are 3 dimensional figures with 4 or more faces, or sides. These polyhedra are reflections of Nature herself, and a study of them provides insight into the way the world is structured. Nature is not only beautiful, but highly intelligent. As you explore the polyhedra in this book, this will become apparent over and over again.
The book contains a geometric explanation of the Phi Ratio and Fibonacci series, and a detailed analysis of the pentagon, which forms the basis for many of these solids. The pentagon is composed entirely of Phi relationships, and is integral to a proper understanding of sacred geometry.
With over 140 full-color illustrations, this book is perfect for teachers and students of geometry alike. It is a must for those who are serious about sacred geometry.
This book is dedicated to those who can appreciate the logic of numbers and the beauty of nature, for they are both aspects of the same unifying principle.
Prerequisites: knowledge of simple algebra and elementary trigonometry. No brainiac math skills required Only the ability to appreciate nature's own logic.
Book #1 in the Geometric Explorations Series
From Loving Healing Press (www.LovingHealing.com)
Автор: Winfried Bruns; Joseph Gubeladze Название: Polytopes, Rings, and K-Theory ISBN: 1441926178 ISBN-13(EAN): 9781441926173 Издательство: Springer Рейтинг: Цена: 23058.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book examines interactions of polyhedral discrete geometry and algebra. What makes this book unique is the presentation of several central results in all three areas of the exposition - from discrete geometry, to commutative algebra, and K-theory.
