38 citations · 101 across the 15 of their papers we have counts for
8 papers · 1 filter
Polyhedral surfaces of high genus
Günter M. Ziegler
The construction of the COMBINATORIAL data for a surface with n vertices of maximal genus is a classical problem: The maximal genus g=[(n-3)(n-4)/12] was achieved in the famous ``M…
Convex Polytopes: Extremal Constructions and f-Vector Shapes
Günter M. Ziegler
These lecture notes treat some current aspects of two closely interrelated topics from the theory of convex polytopes: the shapes of f-vectors, and extremal constructions. The firs…
Projected Products of Polytopes
Günter M. Ziegler
We construct a 2-parameter family of 4-dimensional polytopes with extreme combinatorial structure: In this family, the ``fatness'' of the f-vector gets arbitrarily close to 9, the…
On the Monotone Upper Bound Problem
Julian Pfeifle, Günter M. Ziegler
The Monotone Upper Bound Problem asks for the maximal number M(d,n) of vertices on a strictly-increasing edge-path on a simple d-polytope with n facets. More specifically, it asks…
The -Construction for Lattices, Spheres and Polytopes
Andreas Paffenholz, Günter M. Ziegler
We describe and analyze a new construction that produces new Eulerian lattices from old ones. It specializes to a construction that produces new strongly regular cellular spheres (…
Convex Hulls, Oracles, and Homology
Michael Joswig, G"unter M. Ziegler
This paper presents a new algorithm for the convex hull problem, which is based on a reduction to a combinatorial decision problem POLYTOPE-COMPLETENESS-COMBINATORIAL, which in tur…