6 papers · 1 filter
Bisections of mass assignments by parallel hyperplanes
Nikola Sadovek, Pablo Soberón
In this paper, we prove a result on the bisection of mass assignments by parallel hyperplanes on Euclidean vector bundles. Our methods consist of the development of a novel lifting…
Complex analogues of the Tverberg--Vrećica conjecture and central transversal theorems
Nikola Sadovek, Pablo Soberón
The Tverberg--Vrećica conjecture claims a broad generalization of Tverberg's classical theorem. One of its consequences, the central transversal theorem, extends both the centerpoi…
Tverberg's theorem and multi-class support vector machines
Pablo Soberón
We show how, using linear-algebraic tools developed to prove Tverberg's theorem in combinatorial geometry, we can design new models of multi-class support vector machines (SVMs). T…
Extensions of discrete Helly theorems for boxes
Timothy Edwards, Pablo Soberón
We prove extensions of Halman's discrete Helly theorem for axis-parallel boxes in . Halman's theorem says that, given a set in , if is a finite…
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…
Improved Tverberg theorems for certain families of polytopes
Pablo Soberón, Shira Zerbib
A theorem of Grünbaum, which states that every -polytope is a refinement of an -simplex, implies the following generalization of Tverberg's theorem: if is a linear functi…