9 papers
Blocking codimension-one simplices on the moment curve
Pablo Soberón
We study , the minimum number of points needed to meet the relative interior of every -simplex spanned by an -point set in general position in . In…
Selection-structure generalizations of the Borsuk-Ulam theorem
Pablo Soberón
We prove Borsuk-Ulam-type results governed by selection structures. Selection structures extend the matroidal framework for colorful theorems in discrete geometry and include non-m…
KKM theorems and discrete geometry beyond matroids
Pablo Soberón
We introduce selection structures, a topological framework that extends the role played by color classes and matroids in discrete geometry and KKM theorems. Selection structures al…
Bisecting masses with families of parallel hyperplanes
Alfredo Hubard, Pablo Soberón
We prove a common generalization of several mass partition results using hyperplane arrangements to split into two sets. Our main result implies the ham sandwich the…
Tverberg cores and Kalai's cascade conjecture
Pablo Soberón
We study topological analogues of Kalai's cascade conjecture. Given a continuous map from an -simplex to , let be the set of points contained in the images…
Complex analogues of the Tverberg--VreÄica conjecture and central transversal theorems
Nikola Sadovek, Pablo Soberón
The Tverberg--VreÄica conjecture claims a broad generalization of Tverberg's classical theorem. One of its consequences, the central transversal theorem, extends both the centerpo…