Günter M. Ziegler | Academic Influence

Günter M. Ziegler's AcademicInfluence.com Rankings

Günter M. Ziegler

Mathematics

#428

World Rank

#860

Historical Rank

Combinatorics

#15

World Rank

#19

Historical Rank

Geometry

#26

World Rank

#52

Historical Rank

Measure Theory

#916

World Rank

#1198

Historical Rank

mathematics Degrees

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Mathematics

Why Is Günter M. Ziegler Influential?

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According to Wikipedia, Günter Matthias Ziegler is a German mathematician who has been serving as president of the Free University of Berlin since 2018. Ziegler is known for his research in discrete mathematics and geometry, and particularly on the combinatorics of polytopes.

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Günter M. Ziegler's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Lectures on Polytopes (1994) (3427)
Oriented Matroids (2004) (232)
Bounds for Lattice Polytopes Containing a Fixed Number of Interior Points in a Sublattice (1991) (187)
Discrete Differential Geometry (2008) (158)
Higher bruhat orders and cyclic hyperplane arrangements (1993) (135)
Homotopy types of subspace arrangements via diagrams of spaces (1993) (133)
Basic Properties of Convex Polytopes (2004) (130)
Hyperplane arrangements with a lattice of regions (1990) (129)
Lectures on 0/1-Polytopes (1999) (128)
Combinatorial stratification of complex arrangements (1992) (119)
Homotopy colimits – comparison lemmas for combinatorial applications (1999) (111)
Matroid Applications: Introduction to Greedoids (1992) (107)
Topological lower bounds for the chromatic number: A hierarchy (2002) (101)
Generalized Kneser coloring theorems with combinatorial proofs (2001) (98)
Realization spaces of 4-polytopes are universal (1995) (98)
Optimal bounds for the colored Tverberg problem (2009) (94)
Broken circuit complexes: Factorizations and generalizations (1991) (89)
Many non-equivalent realizations of the associahedron (2011) (83)
Oriented Matroids: Notation (1999) (83)
Kissing numbers, sphere packings, and some unexpected proofs (2004) (79)
Shelling Polyhedral 3-Balls and 4-Polytopes (1998) (78)
Teaching and Learning “ What is Mathematics ” (2014) (76)
0/1-Integer Programming: Optimization and Augmentation are Equivalent (1995) (74)
Polytopes : combinatorics and computation (2000) (74)
Neighborly Cubical Polytopes (1998) (73)
Extension spaces of oriented matroids (1993) (68)
Convex equipartitions via Equivariant Obstruction Theory (2012) (67)
Combinatorial construction of logarithmic differential forms (1989) (65)
Shellability of chessboard complexes (1994) (64)
Tverberg plus constraints (2014) (64)
Randomized Simplex Algorithms on Klee-Minty Cubes (1994) (64)
Gröbner bases of lattices, corner polyhedra, and integer programming. (1995) (60)
Beyond the Borsuk–Ulam Theorem: The Topological Tverberg Story (2016) (57)
Projections of polytopes and the generalized baues conjecture (1996) (57)
On the Maximal Width of Empty Lattice Simplices (2000) (56)
Decompositions of simplicial balls and spheres with knots consisting of few edges (2000) (56)
On locally constructible spheres and balls (2009) (55)
Optimal bounds for a colorful Tverberg--Vrecica type problem (2009) (55)
Coloring Hamming Graphs, Optimal Binary Codes, and the 0/1-Borsuk Problem in Low Dimensions (2001) (53)
The problem of the thirteen spheres (1998) (52)
Matroid representations and free arrangements (1990) (52)
Many triangulated 3-spheres (2002) (49)
Face numbers of 4-Polytopes and 3-Spheres (2002) (45)
Fat 4-polytopes and fatter 3-spheres (2002) (45)
Tverberg’s Theorem at 50: Extensions and Counterexamples (2016) (43)
Hilbert Bases, Unimodular Triangulations, and Binary Covers of Rational Polyhedral Cones (1999) (38)
The ideal-valued index for a dihedral group action, and mass partition by two hyperplanes (2007) (38)
Barycenters of polytope skeleta and counterexamples to the Topological Tverberg Conjecture, via constraints (2015) (38)
Counting lattice triangulations (2002) (37)
A Variant of the Buchberger Algorithm for Integer Programming (1997) (36)
Convex Polytopes: Extremal Constructions and f -Vector Shapes (2004) (36)
Combinatorial models for the finite-dimensional Grassmannians (1993) (35)
Projecting Lattice Polytopes Without Interior Lattice Points (2011) (35)
On the difference between real and complex arrangements (1992) (34)
On Kalai’s Conjectures Concerning Centrally Symmetric Polytopes (2007) (33)
Projected products of polygons (2004) (33)
Construction and Analysis of Projected Deformed Products (2007) (32)
3N Colored Points in a Plane (2011) (29)
Equivariant topology of configuration spaces (2012) (28)
Extremal Properties of 0/1-Polytopes (1997) (28)
All toric local complete intersection singularities admit projective crepant resolutions (2001) (27)
Bier Spheres and Posets (2003) (26)
Topology of the Grünbaum–Hadwiger–Ramos hyperplane mass partition problem (2015) (26)
Zonotopes associated with higher Bruhat orders (2001) (26)
On the Height of the Minimal Hilbert Basis (1993) (26)
Maximizing Möbius functions on subsets of Boolean algebras (1994) (26)
Shadows and slices of polytopes (1996) (25)
Generalized Kneser coloring theorems with combinatorial proofs (2002) (24)
The Et-Construction for Lattices, Spheres and Polytopes (2003) (24)
Algebraic combinatorics of hyperplane arrangements (1987) (24)
Matroid Shellability, β-Systems, and Affine Hyperplane Arrangements (1992) (23)
Construction Techniques for Cubical Complexes, Odd Cubical 4-Polytopes, and Prescribed Dual Manifolds (2003) (23)
Nonrational configurations, polytopes, and surfaces (2007) (22)
Inscribable stacked polytopes (2011) (21)
Many projectively unique polytopes (2012) (20)
Unimodular triangulations of dilated 3-polytopes (2013) (19)
“What is Mathematics?” and why we should ask, where one should experience and learn that, and how to teach it (2017) (19)
What is a complex matroid? (1993) (19)
On cohomology algebras of complex subspace arrangements (2000) (18)
Hyperplane mass partitions via relative equivariant obstruction theory (2015) (18)
On a lemma of Littlewood and Offord (2004) (17)
Combinatorics in pure mathematics (1996) (16)
A Census of Flag-vectors of 4-Polytopes (2000) (15)
Shellability of Complexes of Trees (1998) (15)
The Topological Tverberg Theorem and winding numbers (2005) (15)
15 BASIC PROPERTIES OF CONVEX POLYTOPES (2017) (15)
Polyhedral surfaces in wedge products (2009) (14)
Lê Numbers of Arrangements and Matroid Identities (1997) (14)
Polyhedral Surfaces of High Genus (2004) (14)
Extremal Edge Polytopes (2013) (14)
Gröbner Bases and Integer Programming (1999) (14)
The Simplex Algorithm in Dimension Three (2003) (14)
Singular 0/1-Matrices, and the Hyperplanes Spanned by Random 0/1-Vectors (2003) (14)
Small f-vectors of 3-spheres and of 4-polytopes (2016) (13)
Examples and Counterexamples for the Perles Conjecture (2000) (13)
Convex hulls, oracles, and homology (2003) (13)
On generalized Kneser hypergraph colorings (2005) (12)
Some minimal non-orientable matroids of rank three (1991) (12)
On the Monotone Upper Bound Problem (2003) (12)
A tight colored Tverberg theorem for maps to manifolds (extended abstract) (2011) (11)
Posets with maximal Möbius function (1991) (11)
The face lattice of hyperplane arrangements (1989) (10)
Tetrahedra on deformed spheres and integral group cohomology (2008) (10)
The Great Prime Number Record Races (2004) (10)
Oriented Matroids Today (1998) (10)
Realizing the associahedron: Mysteries and questions (2011) (9)
All toric l.c.i.-singularities admit projective crepant resolutions (1998) (9)
Convex Equipartitions of Colored Point Sets (2017) (9)
Combinatorial Stokes formulas via minimal resolutions (2007) (9)
Face Numbers of Centrally Symmetric Polytopes Produced from Split Graphs (2013) (8)
Oriented Matroids: A Second Orientation Session (1999) (8)
On Complex Highly Regular Embeddings and the Extended Vassiliev Conjecture (2014) (8)
Ziegler Extension Spaces of Oriented Matr iods (1991) (8)
On the poset of partitions of an integer (1986) (8)
Six Topics on Inscribable Polytopes (2015) (8)
Cayley’s formula for the number of trees (2010) (8)
Characterizing Face and Flag Vector Pairs for Polytopes (2018) (8)
Semi-algebraic sets of f-vectors (2017) (7)
Binary Supersolvable Matroids and Modular Constructions (1991) (7)
Alexander Soifer: “The Mathematical Coloring Book. Mathematics of Coloring and the Colorful Life of Its Creators” (2014) (7)
On Free Planes in Lattice Ball Packings (2002) (6)
Euler's polyhedron formula — a starting point of today's polytope theory (2007) (6)
Proofs from THE BOOK (3. ed.) (2004) (6)
Buffon’s needle problem (2010) (6)
Topological representation of dual pairs of oriented matroids (1993) (6)
Typical and Extremal Linear Programs (2004) (6)
Area Difference Bounds for Dissections of a Square into an Odd Number of Triangles (2017) (6)
Simple polytopes without small separators (2015) (6)
Polynomial partitioning for several sets of varieties (2016) (6)
A flag vector of a 3-sphere that is not the flag vector of a 4-polytope ∗ (2015) (6)
Many polytopes with low-dimensional realization space (2012) (5)
Questions About Polytopes (2001) (5)
Additive structures on f-vector sets of polytopes (2017) (5)
THREE PROBLEMS ABOUT 4-POLYTOPES (1994) (5)
Bertrand’s postulate (2014) (5)
Using brouwer’s fixed point theorem (2014) (5)
Three Mathematics Competitions (2011) (5)
Foldable Triangulations of Lattice Polygons (2012) (4)
Lectures on Polytopes: Updates, Corrections, and More (2007) (4)
Counting Periodic Trajectories of Finsler Billiards (2017) (4)
Spaces of convex n-partitions (2015) (4)
Some more amplituhedra are contractible (2018) (4)
Who Solved the Hirsch Conjecture ? (2012) (4)
Zonotopes with Large 2D-Cuts (2007) (4)
On orbit configuration spaces of spheres (2002) (3)
Steinitz’ Theorem for 3-Polytopes (1995) (3)
Ten Problems in Geometry (2013) (3)
Around Brouwer's fixed point theorem (Lecture notes) (2014) (3)
A Small Polyhedral Z-Acyclic 2-Complex in R4 (2007) (3)
CUTTING A PART FROM MANY MEASURES (2017) (3)
The Topological Tverberg Problem and winding numbers (2004) (3)
Three applications of Euler’s formula (2010) (3)
Equivariant Cohomology of Configuration Spaces mod 2: The State of the Art (2020) (3)
Gr obner Bases of Lattices , Corner Polyhedra , and Integer (1995) (3)
Combinatorics of Polytopes - Preface (2000) (3)
Branchings in rooted graphs and the diameter of greedoids (1988) (3)
ON THE DIMENSIONS OF THE REALIZATION SPACES OF POLYTOPES (2020) (2)
Graphs of Polytopes (1995) (2)
Tverberg-Type Theorems for Matroids: A Counterexample and a Proof (2017) (2)
Tetrahedra on Deformed and Integral Group Cohomology (2009) (2)
COMBINATORIAL INSCRIBABILITY OBSTRUCTIONS FOR HIGHER DIMENSIONAL POLYTOPES (2019) (2)
Faces of Polytopes (1995) (2)
6: Oriented matroids (2017) (2)
Cauchy’s rigidity theorem (2004) (2)
Introduction and Examples (1995) (2)
Simple polytopes without small separators, II: Thurston’s bound (2017) (2)
Do I Count?: Stories from Mathematics (2013) (2)
Supersolvable and Modularly Complemented Matroid Extensions (1991) (2)
Sets, functions, and the continuum hypothesis (2010) (2)
The mod 2 equivariant cohomology algebras of configuration spaces -- revised (2020) (2)
Some Almost Exceptional Arrangements (1993) (1)
Decompositions of Simplicial Complexes (2018) (1)
The Polytopes of Cardinality Homogeneous Set Systems (2016) (1)
Barycenters of points that are constrained to a polytope skeleton (2014) (1)
Many non-equivalent realizations of the associahedron (2014) (1)
The Topological Transversal Tverberg Theorem Plus Constraints (2016) (1)
Schlegel Diagrams for 4-Polytopes (1995) (1)
Proofs from the book / Martin Aigner ; Günter M. Ziegler. Including ill. by Karl H. Hofmann (2004) (1)
A new local criterion for the lattice property (1994) (1)
A streetcar named desire (2008) (1)
The Random Edge Rule on Three-Dimensional Linear Programs (2003) (1)
Completing Latin squares (2010) (1)
Face numbers of centrally symmetric polytopes from split graphs (2012) (1)
Mathematics for the People (2012) (1)
Three non-equivalent realizations of the associahedron (2010) (1)
Five-coloring plane graphs (2004) (1)
Representing numbers as sums of two squares (2014) (1)
A Lost Counterexample and a Problem on Illuminated Polytopes (2009) (1)
Equivariant Cohomology of Configuration Spaces Mod 2 (2021) (1)
Hilbert’s third problem: decomposing polyhedra (2010) (1)
Topological and Geometric Combinatorics (2011) (1)
Geometric and Topological Combinatorics (2007) (1)
Convex Equipartitions of Colored Point Sets (2017) (1)
Communicating Mathematics to Society at Large (2011) (1)
The chromatic number of Kneser graphs (2010) (1)
Lines in the plane and decompositions of graphs (2010) (0)
The law of quadratic reciprocity (2010) (0)
For Example: On Occasion of the Fiftieth Anniversary of Gr "unbaum's Convex Polytopes (2019) (0)
J an 2 00 3 The Random Edge Rule on Three-Dimensional Linear Programs 1 ( extended abstract ) (2022) (0)
Duality, Gale Diagrams, and Applications (1995) (0)
Six proofs of the infinity of primes (2010) (0)
The Borromean rings don’t exist (2014) (0)
Permanents and the power of entropy (2014) (0)
Oriented Matroids: From Face Lattices to Topology (1999) (0)
F 1 Geometry processing (2015) (0)
Drei Mal π2/6 (2015) (0)
The Stiefel–Whitney Classes of the Wreath Square of a Vector Bundle (2021) (0)
Pavages de rectangles (2013) (0)
Plus Minus Analogues for Affine Tverberg Type Results (2019) (0)
The Equivariant Cohomology of $${\mathrm {Pe}(\mathbb {R}^{d} ,2^m)}$$ (2021) (0)
Binomial coefficients are (almost) never powers (2001) (0)
On Highly Regular Embeddings: Revised (2021) (0)
“Algebraic Combinatorics ” network (CHRX-CT93-0400) (1995) (0)
Semester Report Ss 05 of Arnold Waßmer Thank You! Field of Research and Results (0)
The fundamental theorem of algebra (2010) (0)
G ] 3 0 N ov 2 00 2 Many Triangulated 3-Spheres (2002) (0)
G ] 2 5 N ov 2 00 3 Many Triangulated 3-Spheres (2003) (0)
The Dickson Algebra (2021) (0)
Book Review: Introduction to geometric probability (1999) (0)
Of friends and politicians (2014) (0)
Randnotizen vom ICM 2010 in Hyderabad (2010) (0)
Amis et politiciens (2013) (0)
Arrangements of Pseudolines (1999) (0)
More Bounds for Highly Regular Embeddings (2021) (0)
Mathematische Annalen Many triangulated 3-spheres (0)
Generalized Kneser Coloring Theorems with Combinatorial Proofs (Erratum) (2005) (0)
Projected Products of Polytopes (2004) (0)
Hu’ng’s Injectivity Theorem (2021) (0)
WITT’S PROOF THAT EVERY FINITE DIVISION RING IS A FIELD (2017) (0)
On the number of simplicial 3-spheres and 4-polytopes with N facets (2008) (0)
Every large point set has an obtuse angle (2010) (0)
Trois applications de la formule d’Euler (2013) (0)
Every finite division ring is a field (2010) (0)
Topological Models for Oriented Matroids (1999) (0)
Simplicial complex models for arrangement complements (2012) (0)
Thirtieth Anniversary Note from the Editors in Chief (2016) (0)
Mathematisches Forschungsinstitut Oberwolfach Report No . 4 / 2007 Geometric and Topological Combinatorics Organised (2007) (0)
The Ptolemaic Epicycles Embedding (2021) (0)
Pigeon-hole and double counting (2014) (0)
2 6 O ct 2 00 9 Optimal bounds for the colored Tverberg problem (2009) (0)
Some irrational numbers (2010) (0)
Three times Π²/6 (2014) (0)
Oriented Matroids: Axiomatics (1999) (0)
Many projectively unique polytopes (2014) (0)
Matar mosques a canonades (2016) (0)
Fiber Polytopes, and Beyond (1995) (0)
The spectral theorem and Hadamard’s determinant problem (2014) (0)
Oriented Matroids: Convex Polytopes (1999) (0)
Random monotone paths on polyhedra (2004) (0)
Alexander Soifer: “The Mathematical Coloring Book. Mathematics of Coloring and the Colorful Life of Its Creators” (2014) (0)
Some more amplituhedra are contractible (2019) (0)
Tverberg-Type Theorems for Matroids: A Counterexample and a Proof (2019) (0)
Oriented Matroids: Constructions (1999) (0)
Identities versus bijections (2014) (0)
Three times π2/6 (2004) (0)
Landau on Chess Tournaments and Google's PageRank (2022) (0)
C O ] 14 M ay 2 00 2 Fat 4-polytopes and fatter 3-spheres (2008) (0)
Four times π 2 /6 (2018) (0)
Following the instructions for preparing the proposal the CVs of Günter Rote 1 and (2012) (0)
Workshop: Combinatorics Table of Contents (2006) (0)
Convex equipartitions via Equivariant Obstruction Theory (2014) (0)
Eidtorial /Termine (2008) (0)
Three famous theorems on finite sets (2010) (0)
Invited talk: Cannons at Sparrows (2012) (0)
Ju n 20 00 Vertex-Facet Incidences of Unbounded Polyhedra (2000) (0)
Workshop: Discrete Geometry Table of Contents (2006) (0)
Cotangent and the Herglotz trick (2010) (0)
Cutting Polygons , Configuration Spaces , and Binomial Coefficients (2017) (0)
Geometry and Connectivity Compression of Triangle Meshes (2006) (0)
Guest Editors’ Foreword (2009) (0)
How to guard a museum (2010) (0)
Algebraie and Geometrie Combinatorics (2018) (0)
Some Current Frontiers of Research (1999) (0)
Supersolvable and Modularly Complemented Matroid Extensions Thomas Wanner (2013) (0)
Plus Minus Analogues for Affine Tverberg Type Results (2019) (0)
Probability makes counting (sometimes) easy (2010) (0)
Tout grand ensemble de points determine un angle obtus (2013) (0)
A theorem of Pólya on polynomials (2001) (0)
One square and an odd number of triangles (2010) (0)
The Dinitz problem (2001) (0)
Thirtieth Anniversary Note from the Editors in Chief (2016) (0)
Das Dinitz-Problem (2015) (0)
Tight and non-tight topological Tverberg type theorems (2014) (0)
Generalized Kneser Coloring Theorems with Combinatorial (2011) (0)
Vier Mal $$ \frac{{\pi^{2} }}{6} $$ (2018) (0)
Snapshots from the History (2021) (0)
Un carré et un nombre impair de triangles (2013) (0)
Conjectures in Combinatorial and Convex Geometry (2010) (0)
Characterizing Face and Flag Vector Pairs for Polytopes (2018) (0)
C O ] 2 0 A ug 2 00 4 The Simplex Algorithm in Dimension Three 1 (2021) (0)
Oriented Matroids: Realizability (1999) (0)
Miscellaneous Calculations (2021) (0)
Maryam Mirzakhani (2017) (0)
Communicating without errors (2014) (0)
Simple polytopes without small separators (2017) (0)
Oriented Matroids: Linear Programming (1999) (0)
Fans, Arrangements, Zonotopes, and Tilings (1995) (0)
The slope problem (2014) (0)
Polytopes, Polyhedra, and Cones (1995) (0)
Proofs from THE BOOK: Putting the Pieces Together Problems (2012) (0)
The finite Kakeya problem (2014) (0)
Simple polytopes without small separators, II: Thurston’s bound (2018) (0)
Polynomial partitioning for several sets of varieties (2016) (0)
ec 2 00 4 Polyhedral surfaces of high genus (2004) (0)
A Cubical 4-Polytope with an Odd Number of Facets (2014) (0)
Proofs from THE BOOK -6/E (2020) (0)
Letter from the New Editors-in-Chief (2011) (0)
In praise of inequalities (2014) (0)
Shellability and the Upper Bound Theorem (1995) (0)
F Visualization (2015) (0)
Four Films by George Csicsery (2010) (0)
0 Ja n 20 03 Convex Hulls , Oracles , and Homology ∗ (2008) (0)
Oriented Matroids: A First Orientation Session (1999) (0)

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Proofs from THE BOOK

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