38 citations · 101 across the 15 of their papers we have counts for
10 papers · 1 filter
The Topological Tverberg Problem and winding numbers
Torsten Schöneborn, Günter M. Ziegler
The Topological Tverberg Theorem claims that any continuous map of a (q-1)(d+1)-simplex to \R^d identifies points from q disjoint faces. (This has been proved for affine maps, for…
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…
The Random Edge Rule on Three-Dimensional Linear Programs
Volker Kaibel, Raphael Mechtel, Micha Sharir +1
The worst-case expected length f(n) of the path taken by the simplex algorithm with the Random Edge pivot rule on a 3-dimensional linear program with n constraints is shown to be b…
Counting Lattice Triangulations
Volker Kaibel, Günter M. Ziegler
We discuss the problem to count, or, more modestly, to estimate the number f(m,n) of unimodular triangulations of the planar grid of size . Among other tools, we employ…