Ziegler, Günter M.Overview
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Most widely held works by
Günter M Ziegler
Proofs from the book
by Martin Aigner
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71 editions published between 1998 and 2013 in 4 languages and held by 1,901 WorldCat member libraries worldwide The mathematical heroes of this book are 'perfect proofs': brilliant ideas, clever connections & wonderful observations that bring new insight & surprising perspectives on basic & challenging problems from number theory, geometry, analysis, combinatorics & graph theory. 30 examples are presented
Lectures on polytopes
by Günter M Ziegler
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36 editions published between 1993 and 2007 in 3 languages and held by 580 WorldCat member libraries worldwide "Based on a graduate course given at the Technische Universität Berlin, these lectures present a wealth of material on the modern theory of convex polytopes."Page 4 of cover
Raisonnements divins quelques démonstrations mathématiques particulièrement élégantes
by Martin Aigner
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20 editions published between 2006 and 2013 in French and English and held by 459 WorldCat member libraries worldwide
Convex polytopes
by Branko Grünbaum
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4 editions published in 2003 in English and held by 340 WorldCat member libraries worldwide "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
Das Buch der Beweise
by Martin Aigner
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Book
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7 editions published between 2001 and 2010 in German and held by 290 WorldCat member libraries worldwide
Polytopes : combinatorics and computation
by Gil Kalai
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11 editions published in 2000 in English and held by 211 WorldCat member libraries worldwide 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
Raisonnements divins
by Martin Aigner
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Book
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6 editions published between 2002 and 2003 in French and held by 76 WorldCat member libraries worldwide Regroupe quelques démonstrations mathématiques choisies pour leur élégance. Différents domaines sont abordés : théorie des nombres, géométrie, analyse combinatoire et théorie des graphes. Propose aussi bien des résultats établis depuis longtemps que des théorèmes récemment démontrés
Do I count? : stories from mathematics
by Günter M Ziegler
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Book
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3 editions published between 2013 and 2014 in English and held by 75 WorldCat member libraries worldwide
Darf ich Zahlen? : Geschichten aus der Mathematik
by Günter M Ziegler
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Book
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5 editions published between 2010 and 2011 in German and Undetermined and held by 69 WorldCat member libraries worldwide
Pi und Co Kaleidoskop der Mathematik
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3 editions published in 2008 in German and Spanish and held by 55 WorldCat member libraries worldwide Mathematik ist eine AuAerst vielseitige, lebendige Wissenschaft. Von ihren groAen Themen wie Zahlen, Unendlichkeiten, Dimensionen und Wahrscheinlichkeiten spannen die Autoren einen Bogen bis hin zu aktuellen Anwendungen in der Logistik, der Finanzwelt, der Kryptographie, der Medizin und anderen Gebieten. Breit gefAchert wie die Mathematik ist auch das Spektrum der BeitrAge. Leicht verstAndliche, unterhaltsame Texte finden sich ebenso wie anspruchsvollere mathematische Herausforderungen. Das Buch ist also eine Einladung an jeden, seinen eigenen Zugang zu dieser spannenden und abenteurreichen Wissenschaft zu finden
Using the BorsukUlam theorem : lectures on topological methods in combinatorics and geometry
by Jiří Matoušek
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11 editions published between 2003 and 2010 in English and held by 53 WorldCat member libraries worldwide A number of important results in combinatorics, discrete geometry, and theoretical computer science have been proved using algebraic topology. While the results are quite famous, their proofs are not so widely understood. They are scattered in research papers or outlined in surveys, and they often use topological notions not commonly known among combinatorialists or computer scientists. This book is the first textbook treatment of a significant part of such results. It focuses on socalled equivariant methods, based on the BorsukUlam theorem and its generalizations. The topological tools are
P [Pi] und Co : Kaleidoskop der Mathematik
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1 edition published in 2008 in German and held by 25 WorldCat member libraries worldwide
Mathematik  Das ist doch keine Kunst!
by Günter M Ziegler
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2 editions published in 2013 in German and held by 20 WorldCat member libraries worldwide
Optimal Bounds for the Colored Tverberg Problem
by Pavle V. M Blagojevic
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1 edition published in 2009 in German and held by 15 WorldCat member libraries worldwide
Oriented matroids
by Anders Björner
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4 editions published between 1993 and 1999 in English and held by 13 WorldCat member libraries worldwide First comprehensive, accessible account; second edition has expanded bibliography and a new appendix surveying recent research
Randomized simplex algorithms on Klee Minty cubes
by Bernd Gärtner
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6 editions published between 1994 and 1998 in English and German and held by 11 WorldCat member libraries worldwide Abstract: "We investigate the behavior of randomized simplex algorithms on special linear programs. For this, we develop combinatorial models for the KleeMinty cubes [16] and similar linear programs with exponential decreasing paths. The analysis of two randomized pivot rules on the KleeMinty cubes leads to (nearly) quadratic lower bounds for the complexity of linear programming with random pivots. Thus we disprove two bounds conjectured in the literature. At the same time, we establish quadratic upper bounds for random pivots on the linear programs under investigation. This motivates the question whether some randomized pivot rules possibly have quadratic worstcase behavior on general linear programs."
El libro de las demostraciones
by Martin Aigner
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2 editions published in 2005 in Spanish and held by 10 WorldCat member libraries worldwide
Shellability of chessboard complexes
by Günter M Ziegler
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4 editions published between 1992 and 1998 in English and German and held by 8 WorldCat member libraries worldwide The notion of vertex decomposability is a very convenient tool to prove shellability of such combinatorially defined simplicial complexes. We establish a relation between vertex decomposability and the CL shellability technique (for posets) of Björner & Wachs."
Extension spaces of oriented matriods
by Bernd Sturmfels
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5 editions published in 1991 in English and German and held by 8 WorldCat member libraries worldwide Abstract: "We study the space of all extensions of a real hyperplance arrangement by a new pseudohyperplane, and, more generally, of an oriented matroid by a new element. The question whether this space has the homotopy type of a sphere is a special case of the 'Generalized Baues Problem' of Billera, Kapranov & Sturmfels, via the BohneDress Theorem on zonotopal tilings. We prove that the extension space is spherical for the class of strongly euclidean oriented matroids. This class includes the alternating matroids and all oriented matroids of rank at most 3 or of corank at most 2. In general it is not even known whether the extension space is connected. We show that the subspace of realizable extensions is always connected but not necessarily spherical."
Discrete differential geometry : [Oberwolfach Seminar "Discrete Differential Geometry" held in May  June 2004]
by Seminar "Discrete differential geometry"
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1 edition published in 2008 in English and held by 8 WorldCat member libraries worldwide more
fewer
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Associated Subjects
Algebra Algebraic topology Beutelspacher, Albrecht Combinatorial analysis Combinatorial geometry Combinatorial optimization Computational complexity Computer science Convex polytopes Discrete geometry Distribution (Probability theory) Evidence Geometry Geometry, Differential Germany Global analysis (Mathematics) Graph theory Information theory Italy Linear programming Mathematical recreations Mathematicians Mathematics MathematicsStudy and teaching Matroids Number theory Oriented matroids Polytopes Proof theory Reasoning

Alternative Names
Cigler, Ginter 1963
Ziegler, G. 1963
Ziegler, G.M.
Ziegler, G. M. 1963
Ziegler, Günter 1963
Ziegler, Günter M.
Ziegler, Gunter M, 1963
Ziegler, M. 1963
ツィーグラー, G. M
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