Periodica Mathematica Hungarica

, Volume 16, Issue 2, pp 135–138 | Cite as

A vector-sum theorem in two-dimensional space

  • I. Bárány
  • V. S. Grinberg


Given a finite setX of vectors from the unit ball of the max norm in the twodimensional space whose sum is zero, it is always possible to writeX = {x1, ⋯, xn} in such a way that the first coordinates of each partial sum\(\mathop \Sigma \limits_1^k x_i \) lie in [−1, 1] and the second coordinates lie in [−C, C] whereC is a universal constant.

AMS (MOS) subject classifications (1980)

Primary 52A40 Secondary 05A05 

Key words and phrases

Bounded partial sums reordering of a series 


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Copyright information

© Akadémiai Kiadó 1985

Authors and Affiliations

  • I. Bárány
    • 1
  • V. S. Grinberg
    • 2
  1. 1.MTA Matematikai Kutató IntézetBudapestHungary
  2. 2.Harkov 58USSR

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