14 citations · 31 across the 8 of their papers we have counts for
9 papers · 1 filter
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…