3 papers
math.MG2015
Small subset sums
Gergely Ambrus, Imre Barany, Victor Grinberg
Let ||.|| be a norm in R^d whose unit ball is B. Assume that V\subset B is a finite set of cardinality n, with \sum_{v \in V} v=0. We show that for every integer k with 0 \le k \le…
math.CO2013
Block Partitions of Sequences
Imre Bárány, Victor S. Grinberg
Given a sequence A=(a1,...,an) of real numbers, a block B of the A is either a set B={ai,...,aj} where i<=j or the empty set. The size b of a block B is the sum of its elements. We…
math.CO2013
2013 Unit Vectors in the Plane
Imre Barany, Boris D. Ginzburg, Victor S. Grinberg
Given a norm on the plane and 2013 unit vectors in this norm, there is a signed sum of these vectors whose norm is at most one.