38 citations · 101 across the 15 of their papers we have counts for
7 papers · 1 filter
Bier spheres and posets
Anders Björner, Andreas Paffenholz, Jonas Sjöstrand +1
In 1992 Thomas Bier presented a strikingly simple method to produce a huge number of simplicial (n-2)-spheres on 2n vertices as deleted joins of a simplicial complex on n vertices…
Construction techniques for cubical complexes, odd cubical 4-polytopes, and prescribed dual manifolds
Alexander Schwartz, Guenter M. Ziegler
We provide a number of new construction techniques for cubical complexes and cubical polytopes, and thus for cubifications (hexahedral mesh generation). As an application we obtain…
The Simplex Algorithm in Dimension Three
Volker Kaibel, Rafael Mechtel, Micha Sharir +1
We investigate the worst-case behavior of the simplex algorithm on linear programs with three variables, that is, on 3-dimensional simple polytopes. Among the pivot rules that we c…
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…