2 citations · 3 across the 3 of their papers we have counts for
4 papers
Coefficients and Roots of Ehrhart Polynomials
M. Beck, J. A. De Loera, M. Develin +2
The Ehrhart polynomial of a convex lattice polytope counts integer points in integral dilates of the polytope. We present new linear inequalities satisfied by the coefficients of E…
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…
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…
Kalai's squeezed 3-spheres are polytopal
Julian Pfeifle
In 1988, Kalai extended a construction of Billera and Lee to produce many triangulated (d-1)-spheres. In fact, in view of upper bounds on the number of simplicial d-polytopes by Go…