6 citations · 10 across the 6 of their papers we have counts for
7 papers
The VC dimension of partial concept classes via Radon's theorem
Grigory Ivanov, Attila Jung, Márton Naszódi
Following Alon, Hanneke, Holzman, and Moran (FOCS 2021), we define a partial concept class (PCC) as a family of partial functions \(f: V\to\{0,1,\ast\}\); equivalently, its concept…
Higher rank antipodality
Márton Naszódi, Zsombor Szilágyi, Mihály Weiner
Motivated by general probability theory, we say that the set in is \emph{antipodal of rank }, if for any elements , there is an…
Quantitative Steinitz theorem: A spherical version
Grigory Ivanov, Márton Naszódi
Steinitz's theorem states that if the origin belongs to the interior of the convex hull of a set , then there are at most points of whos…
On Helly numbers of exponential lattices
Gergely Ambrus, Martin Balko, Nóra Frankl +2
Given a set , define the \emph{Helly number of }, denoted by , as the smallest positive integer , if it exists, for which the following statem…
Functional John and Löwner conditions for pairs of log-concave functions
Grigory Ivanov, Márton Naszódi
John's fundamental theorem characterizing the largest volume ellipsoid contained in a convex body in has seen several generalizations and extensions. One directi…
Quantitative Steinitz Theorem: A polynomial bound
Grigory Ivanov, Márton Naszódi
The classical Steinitz theorem states that if the origin belongs to the interior of the convex hull of a set , then there are at most points of who…
Contacts in totally separable packings in the plane and in high dimensions
Márton Naszódi, Konrad J. Swanepoel
We study the contact structure of totally separable} packings of translates of a convex body in , that is, packings where any two touching bodies have a separatin…