M. Naszódi

activity

20222026

most citedQuantitative Steinitz Theorem: A polynomial bound

6 citations · 10 across the 6 of their papers we have counts for

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math.MG2023★ 1 cited

Higher rank antipodality

Márton Naszódi, Zsombor Szilágyi, Mihály Weiner

Motivated by general probability theory, we say that the set $S$ in $R^{d}$ is \emph{antipodal of rank $k$ }, if for any $k + 1$ elements $q_{1}, \dots q_{k + 1} \in S$ , there is an…

math.MG2023

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 $Q \subset R^{d}$ , then there are at most $2 d$ points $Q^{'}$ of $Q$ whos…

math.MG2022★ 3 cited

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 $K$ in $R^{d}$ has seen several generalizations and extensions. One directi…

math.MG2022★ 6 cited

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 $S \subset R^{d}$ , then there are at most $2 d$ points of $S$ who…

math.MG2022

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 $K$ in $R^{d}$ , that is, packings where any two touching bodies have a separatin…