Periodica Mathematica Hungarica

, Volume 22, Issue 3, pp 183–186 | Cite as

The steinitz lemma inl inf∞ sup2

  • W. Banaszczyk


Let (a, b) be a pair of non-negative numbers such that (1)a, b≥1 and (2)a+b≥3. Letu1,...,u n be a sequence of vectors from the set {(x, yR2: |x|, |y|≤1}, withu1+...+u n =0. It is shown that there is a permutation π of indices such that all partial sumsuπ(1)+...+uπ(k) lie in the rectangle |x|≤a, |y|≤b. Conditions (1) and (2) are also necessary.

Mathematics subject classification numbers, (1980)

Primary 52A40 Secondary 05A05 

Key words and phrases

Bounded partial sums rearrangement of vectors Steinitz lemma 


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Copyright information

© Akadémiai Kiadó 1991

Authors and Affiliations

  • W. Banaszczyk
    • 1
  1. 1.Instytut MatematykiUniwersytetu LódzkiegoLódźPoland

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