3 papers
math.CO2026
An elementary proof of Sierksma's conjecture for seven points in the plane
Pablo Soberón
We give a new simple geometric proof that any seven points in the plane have four Tverberg partitions into three sets. This is the only confirmed non-trivial case of Sierksma's con…
math.CO2025
Fair distribution of bundles
Pablo Soberón
In this paper, we study the problem of splitting fairly bundles of items. We show that given bundles with kinds of items in them, it is possible to distribute the value of…
math.CO2025
Partitions of mass assignments with spheres and wedges
Deron Lessure, Pablo Soberón
In this paper, we generalize classic mass partition results dealing with partitions using spheres, parallel hyperplanes, or axis-parallel wedges to the setting of mass assignments.…