Imre B'ar'any

activity

20242026

collaborators

6 papers

math.CO2026

The Volume Helly Theorem in the plane, colorful version

Imre Bárány, Bobby Miraftab, Leonidas Theocharous

We prove a colorful volume Helly theorem for convex sets in $R^{2}$ : There is a constant $V > 0$ such that if $F_{1}, F_{2}, F_{3}, F_{4}$ are fini…

math.CO2026

A point in the interior of the convex hulls

Imre BÃ¡rÃ¡ny, Yun Qi

Steinitz's theorem states that if a point $a \in int conv X$ for a set $X \subset R^{d}$ , then $X$ contains a subset $Y$ of size at most $2 d$ such that $a \in \m…

math.CO2026

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

Antal Balog, Imre BÃ¡rÃ¡ny

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 BÃ¡rÃ¡ny, 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.CO2025

Piercing intersecting convex sets

Imre BÃ¡rÃ¡ny, Travis Dillon, DÃ¶mÃ¶tÃ¶r PÃ¡lvÃ¶lgyi +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.CO2024

A special balancing game, Victor Grinberg's question

Imre BÃ¡rÃ¡ny

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_…

The Volume Helly Theorem in the plane, colorful version

A point in the interior of the convex hulls

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

Balancing games on unbounded sets

Piercing intersecting convex sets

A special balancing game, Victor Grinberg's question

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