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

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3 papers · 1 filter

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 $…

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}

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