7 papers
Volume and Projection Inequalities I: Zonoids and Courtade's Conjecture
Matthieu Fradelizi, Alfredo Hubard, Auttawich Manui +3
We study volume and projection inequalities for zonoids through the multiaffine determinant polynomials that encode their volumes. We show that a log-submodularity conjecture for t…
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…
Degenerate crossing number and signed reversal distance
Niloufar Fuladi, Alfredo Hubard, Arnaud de Mesmay
Given a graph drawn in the plane, the degenerate crossing number of the drawing is the number of points in the plane which are contained in the relative interior of at least two ed…
Crossing lemmas for -systems of arcs
Alfredo Hubard, Hugo Parlier
We show a generalization of the crossing lemma for multi-graphs drawn on orientable surfaces in which pairs of edges are assumed to be drawn by non-homotopic simple arcs which pair…
Crossing numbers of dense graphs on surfaces
Alfredo Hubard, Arnaud de Mesmay, Hugo Parlier
In this paper, we provide upper and lower bounds on the crossing numbers of dense graphs on surfaces, which match up to constant factors. First, we prove that if is a dense eno…
Crossing number inequalities for curves on surfaces
Alfredo Hubard, Hugo Parlier
We prove that, as grows, any family of homotopically distinct closed curves on a surface induces a number of crossings that grows at least like . We use this…