18 citations · 54 across the 25 of their papers we have counts for
27 papers
Positive bases, cones, Helly type theorems
Imre Barany
Assume that is a positive integer and $\C$ is a finite collection of convex bodies in . We prove a Helly type theorem: If for every subfamily $\C^*\subset \C$ of si…
Tverberg's theorem, a new proof
Imre Barany
We give a new proof Tverberg's famous theorem: For every set with , there is a partition of into sets such that $\bigcap…
Piercing the chessboard
Gergely Ambrus, Imre Bárány, Péter Frankl +1
We consider the minimum number of lines and needed to intersect or pierce, respectively, all the cells of the chessboard. Determining these values can also…
Pairwise intersecting convex sets and cylinders in
Imre Barany
We prove that given a finite collection of cylinders in with the property that any two them intersect, then there is a line intersecting an fraction of the cylinders whe…
Cells in the box and a hyperplane
Imre Barany, Peter Frankl
It is well-known that a line can intersect at most cells of the chessboard. Here we consider the high dimensional version: how many cells of the -dimensional…
Theorems of Carathéodory, Helly, and Tverberg without dimension
Karim Adiprasito, Imre Bárány, Nabil H. Mustafa +1
We prove a no-dimensional version of Carathédory's theorem: given an -element set , a point $a \in \conv P$, and an integer , , there is a subse…