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math.MG2003
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…
math.MG2003
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 (…
math.MG2003
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…