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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.MG2002★ 1 cited
Many Triangulated 3-Spheres
Julian Pfeifle, Günter M. Ziegler
We construct 2^{Ω(n^{5/4})} combinatorial types of triangulated 3-spheres on n vertices. Since by a result of Goodman and Pollack (1986) there are no more than 2^{O(n log n)} combi…