4 papers · 1 filter
High-dimensional envy-free partitions
Pablo Soberón, Christina Yu
A vast array of envy-free results have been found for the subdivision of one-dimensional resources, such as the interval . The goal is to divide the space into pieces an…
Tverberg Partition Graphs
Deborah Oliveros, Érika Roldán, Pablo Soberón +1
Given a finite set of points in , Tverberg's theorem guarantees the existence of partitions of this set into parts whose convex hulls intersect. We introduce a graph…
Colorful and Quantitative Variations of Krasnosselsky's Theorem
Connor Donovan, Danielle Paulson, Pablo Soberón
Krasnosselsky's art gallery theorem gives a combinatorial characterization of star-shaped sets in Euclidean spaces, similar to Helly's characterization of finite families of convex…
Combinatorial Depth Measures for Hyperplane Arrangements
Patrick Schnider, Pablo Soberón
Regression depth, introduced by Rousseeuw and Hubert in 1999, is a notion that measures how good of a regression hyperplane a given query hyperplane is with respect to a set of dat…