Ziegler, Günter M.
Overview
Works:  91 works in 405 publications in 8 languages and 5,711 library holdings 

Genres:  Anecdotes Popular works 
Roles:  Author, Editor, Contributor 
Classifications:  QA36, 510 
Publication Timeline
.
Most widely held works by
Günter M Ziegler
Proofs from the book by
Martin Aigner(
Book
)
147 editions published between 1998 and 2015 in 9 languages and held by 2,122 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
147 editions published between 1998 and 2015 in 9 languages and held by 2,122 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
Gnter M Ziegler(
Book
)
39 editions published between 1993 and 2007 in 3 languages and held by 596 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
39 editions published between 1993 and 2007 in 3 languages and held by 596 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
Do I count? : stories from mathematics by
Gnter M Ziegler(
Book
)
14 editions published between 2010 and 2014 in 3 languages and held by 530 WorldCat member libraries worldwide
These are stories about numbers, problems, people who do maths, and the places where mathematical discoveries are made (such as desks, libraries, beds, and churches). You'll discover that counting can be quite difficult  for example, news reports claiming that 'bees can count' show that journalists can't count and people who shun 13 must assume that gods can't count
14 editions published between 2010 and 2014 in 3 languages and held by 530 WorldCat member libraries worldwide
These are stories about numbers, problems, people who do maths, and the places where mathematical discoveries are made (such as desks, libraries, beds, and churches). You'll discover that counting can be quite difficult  for example, news reports claiming that 'bees can count' show that journalists can't count and people who shun 13 must assume that gods can't count
Convex polytopes by
Branko Grnbaum(
Book
)
8 editions published in 2003 in English and held by 348 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
8 editions published in 2003 in English and held by 348 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
Polytopes : combinatorics and computation by
Gil Kalai(
Book
)
12 editions published in 2000 in English and held by 200 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
12 editions published in 2000 in English and held by 200 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
Mathematik  das ist doch keine Kunst! by
Gnter M Ziegler(
Book
)
4 editions published in 2013 in German and held by 88 WorldCat member libraries worldwide
Wo wir nur einen Herrnhuter Stern sehen oder einen kunstvollen Knoten, zeigt uns der "Popstar unter den Mathematikern" Günter Ziegler die Mathematik in ihrer ganzen Schönheit. In diesem außergewöhnlichen Buch betrachtet der Geometrieprofessor 24 Bilder, die nur auf den ersten Blick nichts mit Mathematik zu tun haben
4 editions published in 2013 in German and held by 88 WorldCat member libraries worldwide
Wo wir nur einen Herrnhuter Stern sehen oder einen kunstvollen Knoten, zeigt uns der "Popstar unter den Mathematikern" Günter Ziegler die Mathematik in ihrer ganzen Schönheit. In diesem außergewöhnlichen Buch betrachtet der Geometrieprofessor 24 Bilder, die nur auf den ersten Blick nichts mit Mathematik zu tun haben
Using the BorsukUlam theorem : lectures on topological methods in combinatorics and geometry by
Jiř Matoušek(
Book
)
13 editions published between 2003 and 2010 in English and held by 36 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
13 editions published between 2003 and 2010 in English and held by 36 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
Optimal Bounds for the Colored Tverberg Problem by
Pavle V. M Blagojevic(
)
2 editions published in 2009 in German and English and held by 18 WorldCat member libraries worldwide
2 editions published in 2009 in German and English and held by 18 WorldCat member libraries worldwide
Discrete differential geometry by
Alexander I Bobenko(
Book
)
4 editions published in 2008 in English and held by 12 WorldCat member libraries worldwide
Discrete differential geometry is an active mathematical terrain where differential geometry and discrete geometry meet and interact. It provides discrete equivalents of the geometric notions and methods of differential geometry, such as notions of curvature and integrability for polyhedral surfaces. Current progress in this field is to a large extent stimulated by its relevance for computer graphics and mathematical physics. This collection of essays, which documents the main lectures of the 2004 Oberwolfach Seminar on the topic, as well as a number of additional contributions by key participants, gives a lively, multifacetted introduction to this emerging field
4 editions published in 2008 in English and held by 12 WorldCat member libraries worldwide
Discrete differential geometry is an active mathematical terrain where differential geometry and discrete geometry meet and interact. It provides discrete equivalents of the geometric notions and methods of differential geometry, such as notions of curvature and integrability for polyhedral surfaces. Current progress in this field is to a large extent stimulated by its relevance for computer graphics and mathematical physics. This collection of essays, which documents the main lectures of the 2004 Oberwolfach Seminar on the topic, as well as a number of additional contributions by key participants, gives a lively, multifacetted introduction to this emerging field
Randomized simplex algorithms on Klee Minty cubes by
Bernd Grtner(
Book
)
6 editions published in 1994 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."
6 editions published in 1994 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."
Shellability of chessboard complexes by
Gnter M Ziegler(
Book
)
4 editions published between 1992 and 1998 in English and German and held by 8 WorldCat member libraries worldwide
Abstract: "The matchings in a complete bipartite graph form a simplicial complex, which in many cases has strong structural properties. We use an equivalent description as chessboard complexes: the complexes of all nontaking rook positions on chessboards of various shapes. In this paper we construct 'certificate kshapes' [sigma](m, n, k) such that if the shape A contains some [sigma](m, n, k), then the (k1)skeleton of the chessboard complex [delta](A) is vertex decomposable in the sense of Provan & Billera. This covers, in particular, the case of rectangular chessboards A=[m]x[n], for which [delta](A) is vertex decomposable if n [> or =] 2m1, and the [formula]skeleton is vertex decomposable in general
4 editions published between 1992 and 1998 in English and German and held by 8 WorldCat member libraries worldwide
Abstract: "The matchings in a complete bipartite graph form a simplicial complex, which in many cases has strong structural properties. We use an equivalent description as chessboard complexes: the complexes of all nontaking rook positions on chessboards of various shapes. In this paper we construct 'certificate kshapes' [sigma](m, n, k) such that if the shape A contains some [sigma](m, n, k), then the (k1)skeleton of the chessboard complex [delta](A) is vertex decomposable in the sense of Provan & Billera. This covers, in particular, the case of rectangular chessboards A=[m]x[n], for which [delta](A) is vertex decomposable if n [> or =] 2m1, and the [formula]skeleton is vertex decomposable in general
Higher Bruhat orders and cyclic hyperplane arrangements by
Gnter M Ziegler(
Book
)
5 editions published between 1991 and 1992 in English and German and held by 7 WorldCat member libraries worldwide
5 editions published between 1991 and 1992 in English and German and held by 7 WorldCat member libraries worldwide
Extension spaces of oriented matriods by
Bernd Sturmfels(
Book
)
6 editions published in 1991 in English and German and held by 7 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."
6 editions published in 1991 in English and German and held by 7 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."
On the difference between real and complex arrangements by
Gnter M Ziegler(
Book
)
5 editions published between 1991 and 1992 in English and German and held by 7 WorldCat member libraries worldwide
5 editions published between 1991 and 1992 in English and German and held by 7 WorldCat member libraries worldwide
A variant of the Buchberger algorithm for integer programming by
Regina Urbaniak(
Book
)
4 editions published in 1994 in English and German and held by 7 WorldCat member libraries worldwide
Abstract: "In this paper we modify Buchberger's Spair reduction algorithm for computing a Gröbner basis of a toric ideal so as to apply to an integer program in inequality form with fixed right hand sides and fixed upper bounds on the variables. We formulate the algorithm in the original space and interpret the reduction steps geometrically. In fact, three variants of this algorithm are presented and we give elementary proofs for their correctness. A relationship between these (exact) algorithms, iterative improvement heuristics and the KernighanLin procedure is established."
4 editions published in 1994 in English and German and held by 7 WorldCat member libraries worldwide
Abstract: "In this paper we modify Buchberger's Spair reduction algorithm for computing a Gröbner basis of a toric ideal so as to apply to an integer program in inequality form with fixed right hand sides and fixed upper bounds on the variables. We formulate the algorithm in the original space and interpret the reduction steps geometrically. In fact, three variants of this algorithm are presented and we give elementary proofs for their correctness. A relationship between these (exact) algorithms, iterative improvement heuristics and the KernighanLin procedure is established."
Gröbner bases of lattices, corner polyhedra, and integer programming by
Bernd Sturmfels(
Book
)
4 editions published in 1994 in German and English and held by 7 WorldCat member libraries worldwide
Abstract: "We investigate the generating sets ('Gröbner bases') of integer lattices which correspond to the Gröbner bases of the associated binomial ideals. Extending results in [22], we obtain a geometric characterization of the universal Gröbner basis in terms of the vertices and edges of the associated corner polyhedra. We emphasize the special case where the lattice has finite index. In this case the corner polyhedra were studied by Gomory [14], and there is a close connection to the 'group problem in integer programming' [20, p. 363]. We present exponential lower and upper bounds for the size of a reduced Gröbner basis. The initial complex of (the ideal of) a lattice is shown to be dual to the boundary of a certain simple polyhedron."
4 editions published in 1994 in German and English and held by 7 WorldCat member libraries worldwide
Abstract: "We investigate the generating sets ('Gröbner bases') of integer lattices which correspond to the Gröbner bases of the associated binomial ideals. Extending results in [22], we obtain a geometric characterization of the universal Gröbner basis in terms of the vertices and edges of the associated corner polyhedra. We emphasize the special case where the lattice has finite index. In this case the corner polyhedra were studied by Gomory [14], and there is a close connection to the 'group problem in integer programming' [20, p. 363]. We present exponential lower and upper bounds for the size of a reduced Gröbner basis. The initial complex of (the ideal of) a lattice is shown to be dual to the boundary of a certain simple polyhedron."
Oriented matroids by
Anders Bjrner(
Book
)
4 editions published between 1993 and 1999 in English and held by 2 WorldCat member libraries worldwide
First comprehensive, accessible account; second edition has expanded bibliography and a new appendix surveying recent research
4 editions published between 1993 and 1999 in English and held by 2 WorldCat member libraries worldwide
First comprehensive, accessible account; second edition has expanded bibliography and a new appendix surveying recent research
Pi und Co. : Kaleidoskop der Mathematik(
Book
)
3 editions published in 2008 in German and Spanish and held by 1 WorldCat member library 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
3 editions published in 2008 in German and Spanish and held by 1 WorldCat member library 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
Lectures on Polytopes Updated Seventh Printing of the First Edition by
Gnter M Ziegler(
)
2 editions published in 1995 in English and held by 0 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. 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 (FourierMotzkin 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 nonrational polytopes, the BohneDress tiling theorem, the upperbound theorem), and nonextendable shellings)
2 editions published in 1995 in English and held by 0 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. 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 (FourierMotzkin 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 nonrational polytopes, the BohneDress tiling theorem, the upperbound theorem), and nonextendable shellings)
P [Pi] und Co : Kaleidoskop der Mathematik(
)
1 edition published in 2008 in German and held by 0 WorldCat member libraries worldwide
1 edition published in 2008 in German and held by 0 WorldCat member libraries worldwide
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Related Identities
 Aigner, Martin 1942 Author
 Hofmann, Karl Heinrich Illustrator
 Klee, Victor Editor
 Grünbaum, Branko Author
 Kaibel, Volker Editor
 Puech, Nicolas Translator
 Kalai, Gil 1955 Author Editor
 Behrends, Ehrhard 1946 Editor
 Gritzmann, Peter Editor
 Björner, Anders Editor Honoree Author Contributor
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Associated Subjects
Algebra Algebraic topology Beutelspacher, Albrecht Combinatorial analysis Combinatorial enumeration problems Combinatorial geometry Combinatorial optimization Computational complexity Computer algorithms Computer science Convex bodies Convex polytopes Discrete geometry Discrete groups Distribution (Probability theory) Evidence Geometry Geometry, Differential Germany Global analysis (Mathematics) Global differential geometry Graph theory Information theory Integer programming Italy Lattice theory Linear programming Mathematical recreations Mathematicians Mathematics MathematicsStudy and teaching Matroids Number theory Oriented matroids Polytopes Proof theory Reasoning
Alternative Names
Cigler, Ginter 1963
Gnter M. Ziegler doorverwijspagina
Gnter M. Ziegler page d'homonymie d'un projet Wikimdia
Gnter M. Ziegler Wikipedia disambiguation page
Gnter Matias Ziegler desambiguacin de Wikipedia
Gnter Matthias Ziegler pgina de desambiguao de um projeto da Wikimedia
Gnter Ziegler grensida
Gnter Ziegler tysk matematikar
Gnter Ziegler tysk matematiker
Gnter Ziegler Wikipediapekerside
Ziegler, G. 1963
Ziegler, G.M.
Ziegler, G. M. 1963
Ziegler, Gnter 1963
Ziegler, Gnter M.
Ziegler, Gunter M 1963
Ziegler, M. 1963
Гинтер М. Циглер
ツィーグラー, G. M
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