Mathematisches Forschungsinstitut Oberwolfach Report No . 13 / 2004 Discrepancy Theory and Its Applications

@inproceedings{Brny2004MathematischesFO,
  title={Mathematisches Forschungsinstitut Oberwolfach Report No . 13 / 2004 Discrepancy Theory and Its Applications},
  author={Imre B{\'a}r{\'a}ny and Maxim Skriganov},
  year={2004}
}
Balanced partitions of vector sequences Imre Bárány Let d, N ∈ N. Let ‖ · ‖ be any norm on R and B = {v ∈ R : ‖v‖ ≤ 1} its unit ball. Some time ago I proved the following result [2]: Let v1, v2, . . . , vN ⊆ B be a finite sequence of vectors. Then there are signs εi ∈ {−1, 1} such that ∥∥∥∥∥ ∑ i∈[n] εivi ∥∥∥∥∥ ≤ 2d for all n ∈ [N ] = {1, 2, . . . , N}. In… CONTINUE READING