14 citations · 45 across the 16 of their papers we have counts for
6 papers · 1 filter
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…
Isometric and affine copies of a set in volumetric Helly results
John A. Messina, Pablo Soberón
We show that for any compact convex set in and any finite family of convex sets in , if the intersection of every sufficiently small…
A mélange of diameter Helly-type theorems
Travis Dillon, Pablo Soberón
A Helly-type theorem for diameter provides a bound on the diameter of the intersection of a finite family of convex sets in given some information on the diameter of…
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…