14 citations · 45 across the 16 of their papers we have counts for
4 papers · 1 filter
Balanced convex partitions of lines in the plane
Alexander Xue, Pablo Soberón
We prove an extension of a ham sandwich theorem for families of lines in the plane by Dujmović and Langerman. Given two sets of lines each in the plane, we prove that it…
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…
Non-commutative groups as prescribed polytopal symmetries
Alexandru Chirvasitu, Frieder Ladisch, Pablo Soberón
We study properties of the realizations of groups as the combinatorial automorphism group of a convex polytope. We show that for any non-abelian group with a central involution…
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…