Lectures on Polytopes

Lectures on Polytopes

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

Author: Günter M. Ziegler

Publisher: Springer Science & Business Media

ISBN: 038794365X

Category: Mathematics

Page: 370

View: 938

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.
Categories: Mathematics

Lectures in Geometric Combinatorics

Lectures in Geometric Combinatorics

97 , American Mathematical Society , Providence , RI , 2002 . G . M . Ziegler ,
Lectures on Polytopes , Graduate Texts in Mathematics , vol . 152 , Springer -
Verlag , New York , 1995 . [ Stu02 ] [ Zie95 ] poset , 18 refinement , 70 prism , 13 ...

Author: Rekha R. Thomas

Publisher: American Mathematical Soc.

ISBN: 0821841408

Category: Mathematics

Page: 143

View: 193

This book presents a course in the geometry of convex polytopes in arbitrary dimension. It takes readers from the basics of polytope theory to recent developments around secondary and state polytopes arising from point configurations. The most needed concepts are developed from scratch. Text illustrates the interaction among discrete geometry, computational algebra and combinatorics. This book is published in cooperation with IAS/Park City Mathematics Institute.
Categories: Mathematics

Lectures on Discrete Geometry

Lectures on Discrete Geometry

Jiri Matousek is Professor of Computer Science at Charles University in Prague. His research has contributed to several of the considered areas and to their algorithmic applications. This is his third book.

Author: Ji?í Matoušek

Publisher: Springer Science & Business Media

ISBN: 9781461300397

Category: Mathematics

Page: 486

View: 310

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.
Categories: Mathematics

Polytopes Combinations and Computation

Polytopes   Combinations and Computation

J. 37, pp 1–12, 1958 [13] B. GRÜNBAUM, Convex Polytopes, Interscience, New
York, 1967 [14] M. HENK, ... New York, 1975 [22] G.M. ZIEGLER, Lectures on
Polytopes, Graduate Texts in Mathematics 152, Springer-Verlag, 1995; Revised ...

Author: Gil Kalai

Publisher: Birkhäuser

ISBN: 9783034884389

Category: Mathematics

Page: 225

View: 741

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.
Categories: Mathematics

Novel Approaches to Hard Discrete Optimization

Novel Approaches to Hard Discrete Optimization

[27] Hendrick W. Lenstra, Jr,, Factoring integers with elliptic curves, Annals of
Mathematics. Second Series 126 (19s7). no. 3. ... [40] Giinter M. Ziegler, Lectures
on polytopes. Graduate Texts in Mathematics. voI. 152. Springer- Verlag, New
York ...

Author: Panos M. Pardalos

Publisher: American Mathematical Soc.

ISBN: 082188591X

Category: Mathematics

Page: 181

View: 146

During the last decade, many novel approaches have been considered for dealing with computationally difficult discrete optimization problems. Such approaches include interior point methods, semidefinite programming techniques, and global optimization. More efficient computational algorithms have been developed and larger problem instances of hard discrete problems have been solved. This progress is due in part to these novel approaches, but also to new computing facilities and massive parallelism. This volume contains the papers presented at the workshop on ''Novel Approaches to Hard Discrete Optimization''. The articles cover a spectrum of issues regarding computationally hard discrete problems.
Categories: Mathematics

Pure and Applied Mathematics Quarterly

Pure and Applied Mathematics Quarterly

Math . Soc . , Providence , R . I . , 1991 , pp . 387 - 411 . [ 5 ] P . McMullen , The
maximum numbers of faces of a convez polytope , Mathematica 17 ( 1970 ) , 179
... [ 9 ] G . M . Ziegler , Lectures on Polytopes , Graduate Texts in Mathematics ,
Vol .

Author:

Publisher:

ISBN: UOM:39015072604062

Category: Mathematics

Page:

View: 816

Categories: Mathematics

International Mathematical News

International Mathematical News

Ziegler , G. M .: Lectures on Polytopes . ( Graduate Texts in Mathematics 152. )
Springer - Verlag , New York / Berlin / Heidelberg / London / Paris / Tokyo / Hong
Kong / Barcelona / Budapest , 1995 , IX + 370 S. ISBN 3-540-94365 - X , ISBN ...

Author:

Publisher:

ISBN: CORNELL:31924074856976

Category: Mathematics

Page:

View: 902

Categories: Mathematics

Realization Spaces of Polytopes

Realization Spaces of Polytopes

[ 53 ] P . SHOR , Stretchability of pseudolines is NP - hard , in : Applied Geometry
and Discrete Mathematics – The ... [ 65 ] G . M . ZIEGLER , Lectures on Polytopes
, Graduate Texts in Mathematics transformation groups , 18 translations , 18 ...

Author: Jurgen Richter-Gebert

Publisher: Springer Verlag

ISBN: STANFORD:36105017795068

Category: Mathematics

Page: 187

View: 998

Based on a course given to beginning physics, chemistry, and engineering students at the Winterthur Polytechnic Institute, this text approaches the fundamentals of thermodynamics from the view of continuum mechanics. By describing physical processes in terms of the flow and balance of physical quantities, this provides a unified approach to hydraulics, electricity, mechanics and thermodynamics. In this way it becomes clear that the entropy is the fundamental property that is transported in thermal process (what in lay terms would be called 'heat'), and that the temperature is the corresponding potential. The resulting theory of the creation, flow, and balance of entropy provides the foundation of a dynamical theory of heat. Previous knowledge of thermodynamics is not required, but the reader should be familiar with basic electricity, mechanics, and chemistry and should have some knowledge of elementary calculus.
Categories: Mathematics

Linear Inequalities for Flag F vectors of Polytopes

Linear Inequalities for Flag F vectors of Polytopes

[ 38 ] T. Zaslavsky , “ Facing up to arrangements : Face - count formulas for
partitions of space by hyperplanes , ” Memoirs of the American Mathematical
Society 1 ( 1975 ) . [ 39 ] G. Ziegler , Lectures on Polytopes , Graduate Texts in
Mathematics ...

Author: Catherine Anne Stenson

Publisher:

ISBN: CORNELL:31924088881234

Category:

Page: 146

View: 708

First we present some of the history of this problem, along with the necessary mathematical background. We discuss several special classes of polytopes, including simplicials, simples, cubicals, and zonotopes, whose flag f-vectors satisfy inequalities not satisfied by all polytopes.
Categories:

Bulletin of the American Mathematical Society

Bulletin of the American Mathematical Society

Viro , ed . ) , Lecture Notes in Math . , vol . ... [ 17 ] J . Richter - Gebert , Realization
spaces of 4 - polytopes are universal , Preprint 448 / 1995 , Technical University ,
Berlin , 1995 . ... [ 23 ] — , Lectures on polytopes , Graduate Texts in Math . , vol .

Author:

Publisher:

ISBN: UOM:49015003188571

Category: Mathematics

Page:

View: 920

Categories: Mathematics

Israel Journal of Mathematics

Israel Journal of Mathematics

References e [ 1 ] D. W. Barnette , A family of neighborly polytopes , Israel
Journal of Mathematics 39 ( 1981 ) , 127-140 . [ 2 ] F. Holt ... [ 9 ] G. M. Ziegler ,
Lectures on Polytopes , Graduate Texts in Mathematics 152 , Springer , New York
, 1995.

Author: Moʻatsah ha-leʼumit le-meḥḳar ule-fituaḥ (Israel)

Publisher:

ISBN: UCBK:C078274114

Category: Electronic journals

Page:

View: 590

Categories: Electronic journals

Topics in Discrete Geometry

Topics in Discrete Geometry

[ 12 ] E. Miller and B. Sturmfels , Combinatorial Commutative Algebra , Springer
Graduate Texts in Mathematics , to appear . ( 13 ] W. D. ... [ 14 ] J. Richter - Gebert
, Realization Spaces of Polytopes , Springer Lecture Notes in Mathematics , no .

Author: Michael Lee Develin

Publisher:

ISBN: UCAL:C3486359

Category:

Page: 136

View: 644

Categories:

SIAM Journal on Computing

SIAM Journal on Computing

Society for Industrial and Applied Mathematics. ( 33 ) B . KUIJPERS AND ... ( 35 )
J . M . LEE , Introduction to Topological Manifolds , Graduate Texts in Math . ...
397 - 421 . ( 51 ) G . M . ZIEGLER , Lectures on Polytopes , Graduate Texts in
Math .

Author: Society for Industrial and Applied Mathematics

Publisher:

ISBN: UOM:39015065057740

Category: Electronic data processing

Page:

View: 581

Categories: Electronic data processing

A Study of Permutation Polytopes Arising in Combinatorics and Optimization

A Study of Permutation Polytopes Arising in Combinatorics and Optimization

... the plane , Discrete Comput . Geom . , ( 1986 ) , 95-100 . [ 25 ] G.M. Ziegler ,
Lectures on Polytopes , Graduate Texts in Mathematics 152 , Springer - Verlag ,
New York , 1995 . Cornell University Library MAR 0 5 1996 Mathematics Livraiy
71.

Author: Aravamuthan Sarangarajan

Publisher:

ISBN: CORNELL:31924074548565

Category:

Page: 142

View: 270

Categories:

Integer Programming and Combinatorial Optimization

Integer Programming and Combinatorial Optimization

( 2 ] Ziegler , G . M . : Lectures on 0 / 1 - polytopes . ... Math . Programming 45 (
1989 ) 109 - 110 [ 4 ] Bárány , I . , Pór , A . : On 0 - 1 polytopes with many facets .
Adv . Math . 161 ( 2001 ) 209 ... Volume 152 of Graduate Texts in Mathematics .

Author:

Publisher:

ISBN: UOM:39015058879076

Category: Combinatorial optimization

Page:

View: 213

Categories: Combinatorial optimization

Algebraic Geometry Santa Cruz 1995

Algebraic Geometry  Santa Cruz 1995

Gröbner Bases and Conver Polytopes , University Lecture Series 8 , AMS ,
Providence , RI , 1996 . On the Newton polytope of the resultant , J. Algebraic
Combin . 3 ( 1994 ) , 207– ... G. Ziegler , Lectures on Polytopes , Graduate Texts
in Math .

Author: János Kollár

Publisher: American Mathematical Soc.

ISBN: STANFORD:36105022859776

Category: Mathematics

Page: 896

View: 646

This volume contains many of the lectures delivered at the AMS Summer Research Institute on Algebraic Geometry held at the University of California, Santa Cruz in July 1995. The aim of the conference was to provide a comprehensive view of the development of algebraic geometry in the past decade and to lay special emphasis on emerging new directions. The focus of the papers in these volumes is on expository surveys of important areas rather than on technical presentations of new results. These proceedings will be an indispensable reference and guide for researchers in algebraic geometry or nearby fields. Features: Comprehensive coverage of developments over the past decade. Emphasis on new directions and future developments. Connections to related fields. Many expository survey papers.
Categories: Mathematics

Documenta Mathematica

Documenta Mathematica

( Fel01 ] Stefan Felsner , Convex drawings of planar graphs and the order
dimension of 3 - polytopes , Order 18 ( 2001 ) , no . 1 , 19 – 37 . ( Fel02 Stefan ... (
Zie95 ] Günter M . Ziegler , Lectures on polytopes , Graduate Texts in
Mathematics , vol .

Author:

Publisher:

ISBN: UOM:39015057322375

Category: Mathematics

Page:

View: 156

Categories: Mathematics

Nagoya Mathematical Journal

Nagoya Mathematical Journal

( 16 ) K . Yanagawa , Stanley - Reisner rings , sheaves , and Poincaré - Verdier
duality , Math . Res . Lett . , 10 ( 2003 ) , 635 - 650 . ... ( 19 ) G . Ziegler , Lectures
on Polytopes , Graduate Texts in Mathematics , Vol . 152 , Springer , 1995 (
Revised ...

Author:

Publisher:

ISBN: UCSD:31822037410263

Category: Mathematics

Page:

View: 802

Issue for Mar. 1970 dedicated to Professor Katuzi Ono on his 60th birthday with portrait, sketch of his life, and list of mathematical papers.
Categories: Mathematics