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8 papers
A Quantitative Helly-type Theorem: Containment in a Homothet
Grigory Ivanov, Márton Naszódi
We introduce a new variant of quantitative Helly-type theorems: the minimal \emph{"homothetic distance"} of the intersection of a family of convex sets to the intersection of a sub…
Quantitative Fractional Helly and -Theorems
Attila Jung, Márton Naszódi
We consider quantitative versions of Helly-type questions, that is, instead of finding a point in the intersection, we bound the volume of the intersection. Our first main geometri…
Angular measures and Birkhoff orthogonality in Minkowski planes
Márton Naszódi, Vilmos Prokaj, Konrad Swanepoel
Let and be two unit vectors in a normed plane . We say that is Birkhoff orthogonal to if the line through in the direction supports the unit d…
Approximation of the average of some random matrices
Grigory Ivanov, Márton Naszódi, Alexandr Polyanskii
Rudelson's theorem states that if for a set of unit vectors and positive weights , we have that is the identity operator on …
Colorful Helly-type Theorems for the Volume of Intersections of Convex Bodies
Gábor Damásdi, Viktória Földvári, Márton Naszódi
We prove the following Helly-type result. Let be finite families of convex bodies in . Assume that for any colorful selection o…
On the volume bound in the Dvoretzky--Rogers lemma
Ferenc Fodor, Márton Naszódi, Tamás Zarnócz
The classical Dvoretzky--Rogers lemma provides a deterministic algorithm by which, from any set of isotropic vectors in Euclidean -space, one can select a subset of vectors…