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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
Article

Abstract

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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References

  1. [1]
    I. Bárány, A vector-sum theorem and its application to improving flow shop guarantees,Math. Oper. Res. 6 (1981), 445–452.MR 82i: 90057Google Scholar
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    I. S. Belov andJa. N. Stolin, Algoritm v odnomaršrutnoi zadače kalendarnogo planirovanija (An algorithm for the single-route scheduling problem), Matematičeskaja èkonomika i funkcional'nyi analiz, Nauka, Moskva, 1974; 248–257.MR 56: 17780Google Scholar
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    V. S. Grinberg andS. V. Sevast'janov, O veličine konstanty Steinica (On the value of the Steinitz constant),Funkcional. Anal. i Priložen. 14/2 (1980), 56–57.MR 81h: 52008Google Scholar
  4. [4]
    E. Steinitz, Bedingt konvergente Reihen und konvexe Systeme,J. Reine Angew. Math. 143 (1913), 128–175.Google Scholar

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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