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math.CO2019
Quantitative combinatorial geometry for concave functions
Sherry Sarkar, Alexander Xue, Pablo Soberón
We prove several exact quantitative versions of Helly's and Tverberg's theorems, which guarantee that a finite family of convex sets in has a large intersection. Our results…
math.CO2019
Prescribing Symmetries and Automorphisms for Polytopes
Egon Schulte, Pablo Soberón, Gordon Ian Williams
We study finite groups that occur as combinatorial automorphism groups or geometric symmetry groups of convex polytopes. When is a subgroup of the combinatorial automorphism gr…