Imre Bárány

activity

20142025

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3 papers · 1 filter

math.CO2025

Excursions in Sylvester-Gallai land

Imre Barany, Julia Q. Du, Dan Schwarz +2

The Sylvester-Gallai theorem states that for a finite set of points in the plane, if every line determined by any two of these points also contains a third, then the set is necessa…

math.CO2023

A matrix version of the Steinitz lemma

Imre Barany

The Steinitz lemma, a classic from 1913, states that $a_{1}, \dots, a_{n}$ , a sequence of vectors in $R^{d}$ with $\sum_{1}^{n} a_{i} = 0$ , can be rearranged so that every partial sum of the rea…

math.CO2014

Volumes of convex lattice polytopes and a question of V. I. Arnold

Imre Barany, Liping Yuan

We show by a direct construction that there are at least $exp {c V^{(d - 1) / (d + 1)}}$ convex lattice polytopes in $R^{d}$ of volume $V$ that are different in the sense that no…