Ziegler, Günter M.
Overview
Works:  95 works in 416 publications in 7 languages and 5,954 library holdings 

Genres:  Anecdotes Popular works 
Roles:  Author, Editor, Contributor, Interviewee 
Classifications:  QA36, 510 
Publication Timeline
.
Most widely held works by
Günter M Ziegler
Proofs from the book by
Martin Aigner(
Book
)
100 editions published between 1998 and 2014 in 8 languages and held by 1,704 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
100 editions published between 1998 and 2014 in 8 languages and held by 1,704 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
)
40 editions published between 1993 and 2007 in 3 languages and held by 615 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
40 editions published between 1993 and 2007 in 3 languages and held by 615 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
)
15 editions published between 2010 and 2014 in 3 languages and held by 555 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
15 editions published between 2010 and 2014 in 3 languages and held by 555 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
Das Buch der Beweise by
Martin Aigner(
Book
)
46 editions published between 2002 and 2015 in 3 languages and held by 488 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
46 editions published between 2002 and 2015 in 3 languages and held by 488 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
Convex polytopes by
Branko Grnbaum(
Book
)
9 editions published in 2003 in English and held by 359 WorldCat member libraries worldwide
"The appearance of Grünbaum'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 Grünbaum 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)
9 editions published in 2003 in English and held by 359 WorldCat member libraries worldwide
"The appearance of Grünbaum'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 Grünbaum 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)
Polytopes : combinatorics and computation by
Gil Kalai(
Book
)
12 editions published in 2000 in English and held by 203 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 203 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 89 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 auergewöhnlichen 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 89 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 auergewöhnlichen 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
)
12 editions published between 2003 and 2010 in English and held by 38 WorldCat member libraries worldwide
"The "Kneser conjecture"Posed by Martin Kneser in 1955 in the Jahresbericht der DMV  is an innocentlooking problem about partitioning the ksubsets of an nset into intersecting subfamilies. Its striking solution by L. Lovsz featured an unexpected use of the BorsukUlam theorem, that is, of a genuinely topological result about continuous antipodal maps of spheres. Matousek's lively little textbook now shows that Lovsz' insight as well as beautiful work of many others (such as Vrecica and Zivaljevic, and Sarkaria) have opened up an exciting area of mathematics that connects combinatorics, graph theory, algebraic topology and discrete geometry. What seemed like an ingenious trick in 1978 now presents itself as an instance of the "test set paradigm": to construct configuration spaces for combinatorial problems such that coloring, incidence or transversal problems may be translated into the (non )existence of suitable equivariant maps. The vivid account of this area and its ramifications by Matousek is an exciting, a coherent account of this area of topological combinatorics. It features a collection of mathematical gems written with a broad view of the subject and still with loving care for details. Recommended reading! " Gnter M. Ziegler (Berlin) Zbl. MATH Volume 1060 Productionsno.: 05001
12 editions published between 2003 and 2010 in English and held by 38 WorldCat member libraries worldwide
"The "Kneser conjecture"Posed by Martin Kneser in 1955 in the Jahresbericht der DMV  is an innocentlooking problem about partitioning the ksubsets of an nset into intersecting subfamilies. Its striking solution by L. Lovsz featured an unexpected use of the BorsukUlam theorem, that is, of a genuinely topological result about continuous antipodal maps of spheres. Matousek's lively little textbook now shows that Lovsz' insight as well as beautiful work of many others (such as Vrecica and Zivaljevic, and Sarkaria) have opened up an exciting area of mathematics that connects combinatorics, graph theory, algebraic topology and discrete geometry. What seemed like an ingenious trick in 1978 now presents itself as an instance of the "test set paradigm": to construct configuration spaces for combinatorial problems such that coloring, incidence or transversal problems may be translated into the (non )existence of suitable equivariant maps. The vivid account of this area and its ramifications by Matousek is an exciting, a coherent account of this area of topological combinatorics. It features a collection of mathematical gems written with a broad view of the subject and still with loving care for details. Recommended reading! " Gnter M. Ziegler (Berlin) Zbl. MATH Volume 1060 Productionsno.: 05001
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
Randomized simplex algorithms on Klee Minty cubes by
Bernd Grtner(
Book
)
6 editions published in 1994 in English and German and held by 13 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 13 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."
Discrete differential geometry by
Alexander I Bobenko(
Book
)
3 editions published in 2008 in English and held by 10 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 particip
3 editions published in 2008 in English and held by 10 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 particip
Shellability of chessboard complexes by
Gnter M Ziegler(
Book
)
4 editions published between 1992 and 1998 in English and German and held by 9 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."
4 editions published between 1992 and 1998 in English and German and held by 9 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."
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 8 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 8 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."
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 8 WorldCat member libraries worldwide
5 editions published between 1991 and 1992 in English and German and held by 8 WorldCat member libraries worldwide
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 8 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 8 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."
Extension spaces of oriented matriods by
Bernd Sturmfels(
Book
)
6 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."
6 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."
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
 Kaibel, Volker Editor
 Grünbaum, Branko Author
 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 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 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
Gnter M. Ziegler doorverwijspagina
Gnter M. Ziegler German mathematician
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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