14 citations · 45 across the 16 of their papers we have counts for
21 papers
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…
Fair distributions for more participants than allocations
Pablo Soberón
We study the existence of fair distributions when we have more guests than pieces to allocate, focusing on envy-free distributions among those who receive a piece. The conditions o…
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…