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math.MG2023

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…