14 citations · 45 across the 16 of their papers we have counts for
14 papers · 1 filter
Variations of Helly's theorem for convex splinters
Pablo Soberón, Iris Ye
A convex splinter is a union of convex sets in such that every minimal affine dependent set of contained in is contained in one of the sets. T…
Bisections of mass assignments using flags of affine spaces
Ilani Axelrod-Freed, Pablo Soberón
We use recent extensions of the Borsuk--Ulam theorem for Stiefel manifolds to generalize the ham sandwich theorem to mass assignments. A -dimensional mass assignment continuousl…
Lifting methods in mass partition problems
Pablo Soberón, Yuki Takahashi
Many results in mass partitions are proved by lifting to a higher-dimensional space and dividing the higher-dimensional space into pieces. We extend such methods to…
Generalizations of the Yao-Yao partition theorem and the central transversal theorem
Michael N. Manta, Pablo Soberón
We generalize the Yao-Yao partition theorem by showing that for any smooth measure in there exist equipartitions using convex regions such that every hyperplan…
A survey of mass partitions
Edgardo Roldán-Pensado, Pablo Soberón
Mass partition problems describe the partitions we can induce on a family of measures or finite sets of points in Euclidean spaces by dividing the ambient space into pieces. In thi…
Tverberg's theorem, disks, and Hamiltonian cycles
Pablo Soberón, Yaqian Tang
For a finite set of points in the plane and a graph with vertices on consider the disks with diameters induced by the edges. We show that for any odd set there exists a…
Tolerance for colorful Tverberg partitions
Sherry Sarkar, Pablo Soberón
Tverberg's theorem bounds the number of points needed for the existence of a partition into parts whose convex hulls intersect. If the points are colored with $N…
The topological Tverberg problem beyond prime powers
Florian Frick, Pablo Soberón
Tverberg-type theory aims to establish sufficient conditions for a simplicial complex such that every continuous map maps points from pairwise d…
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…
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…
A Note on the Maximum Rectilinear Crossing Number of Spiders
Joshua Fallon, Kirsten Hogenson, Lauren Keough +3
The maximum rectilinear crossing number of a graph is the maximum number of crossings in a good straight-line drawing of in the plane. In a good drawing any two edges inter…
Tverberg's theorem is 50 years old: a survey
Imre Bárány, Pablo Soberón
This survey presents an overview of the advances around Tverberg's theorem, focusing on the last two decades. We discuss the topological, linear-algebraic, and combinatorial aspect…
Cutting a part from many measures
Pavle V. M. Blagojević, Nevena Palić, Pablo Soberón +1
Holmsen, Kynčl and Valculescu recently conjectured that if a finite set with points in that is colored by different colors can be partitioned into $…
Thieves can make sandwiches
Pavle V. M. Blagojević, Pablo Soberón
We prove a common generalization of the Ham Sandwich theorem and Alon's Necklace Splitting theorem. Our main results show the existence of fair distributions of measures in $R^…