Imre B'ar'any

activity

20212026

collaborators

6 papers

math.CO2026

The integer hull of the set ${(x, y) \in R^{2} : x y \geq N}$

Antal Balog, Imre Bárány

The integer convex hull $I (H_{N})$ of the set $H_{N} = {(x, y) \in R^{2} : x y \geq N}$ is the convex hull of the lattice points in $H_{N}$ . The vertices of $I (H_{N})$ lie in the square $…

math.CO2025

Balancing games on unbounded sets

Imre Bárány, Jeck Lim

For a finite set $V \subset R^{n}$ , a set $T \subset R^{n}$ is called $V$ -closed if $t \in T$ and $v \in V$ imply that either $t + v \in T$ or $t - v \in T$ . The set $P(V):=\…

math.CO2024

A special balancing game, Victor Grinberg's question

Imre Bárány

In a vector balancing game, on step $k$ player 1 chooses a unit vector $v_{k}$ and player 2 chooses a sign $ε_{k} \in {- 1, 1}$ , and the position after $n$ steps is $z_n=\sum_…

math.CO2024

Piercing intersecting convex sets

Imre Bárány, Travis Dillon, Dömötör Pálvölgyi +1

Assume two finite families $A$ and $B$ of convex sets in $R^{3}$ have the property that $A \cap B \neq = \emptyset$ for every $A \in A$ and $B\in \math…

math.CO2021

Universal sequences of lines in $R^{d}$

Imre Bárány, Gil Kalai, Attila Pór

One of the most important and useful examples in discrete geometry is a finite sequence of points on the moment curve $γ (t) = (t, t^{2}, t^{3}, \dots, t^{d})$ or, more generally, on a {\it st…

math.CO2021

Helly-type Problems

Imre Bárány, Gil Kalai

In this paper, we present a variety of problems in the interface between combinatorics and geometry around the theorems of Helly, Radon, Carathéodory, and Tverberg. Through these p…

The integer hull of the set {(x,y)∈R2:xy≥N}