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Optimal bounds for a colorful Tverberg--Vrecica type problem
Pavle Blagojevic, Benjamin Matschke, Gunter Ziegler
We prove the following optimal colorful Tverberg-Vrecica type transversal theorem: For prime r and for any k+1 colored collections of points C^l of size |C^l|=(r-1)(d-k+1)+1 in R^d…
Optimal bounds for the colored Tverberg problem
Pavle V. M. Blagojević, Benjamin Matschke, Günter M. Ziegler
We prove a "Tverberg type" multiple intersection theorem. It strengthens the prime case of the original Tverberg theorem from 1966, as well as the topological Tverberg theorem of B…
Polyhedral Surfaces in Wedge Products
Thilo Rörig, Günter M. Ziegler
We introduce the wedge product of two polytopes. The wedge product is described in terms of inequality systems, in terms of vertex coordinates as well as purely combinatorially, fr…
A Lost Counterexample and a Problem on Illuminated Polytopes
Ronald F. Wotzlaw, Günter M. Ziegler
In a Note added in proof to a 1984 paper, Daniel A. Marcus claimed to have a counterexample to his conjecture that a minimal positively k-spanning vector configuration in R^m has s…
On locally constructible spheres and balls
Bruno Benedetti, Günter M. Ziegler
Durhuus and Jonsson (1995) introduced the class of "locally constructible" (LC) 3-spheres and showed that there are only exponentially-many combinatorial types of simplicial LC 3-s…