Imre B'ar'any

activity

20092026

most citedIntrinsic volumes of inscribed random polytopes in smooth convex bodies

18 citations · 19 across the 10 of their papers we have counts for

collaborators

11 papers

math.CO2026

Line arrangements, bounded cells, and discrepancy

Imre Bárány

An arrangement of $n$ lines in the plane defines cells, i.e., connected components of the complement of the arrangement. Answering a question of Volkmar Welker we show that, apart…

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

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.CO2025

A point in the interior of the convex hulls

Imre Bárány, 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.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.CO2023★ 1 cited

Same average in every direction

Imre Bárány, Gábor Domokos

Given a polytope $P \subset R^{3}$ and a non-zero vector $z \in R^{3}$ , the plane ${x \in R^{3} : z x = t}$ intersects $P$ in convex polygon $P (z, t)$ for $t \in [t^{-}, t^{+}]$ where $t^-=\min \{z…

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…

math.MG2009★ 18 cited

Intrinsic volumes of inscribed random polytopes in smooth convex bodies

Imre Bárány, Ferenc Fodor, Viktor Vígh

Let $K$ be a $d$ dimensional convex body with a twice continuously differentiable boundary and everywhere positive Gauss-Kronecker curvature. Denote by $K_{n}$ the convex hull of $n$ …

Line arrangements, bounded cells, and discrepancy

The Volume Helly Theorem in the plane, colorful version

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

Balancing games on unbounded sets

A point in the interior of the convex hulls

A special balancing game, Victor Grinberg's question

Piercing intersecting convex sets

Same average in every direction

Universal sequences of lines in Rd

Helly-type Problems

Intrinsic volumes of inscribed random polytopes in smooth convex bodies

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

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