Balancing vectors in the max norm

Abstract

Let v1, ..., v n be vectors inR n of max norm at most one. It is proven that there exists a choice of signs for which all partial sums have max norm at mostKn 1/2. It is further shown that such a choice of signs must be anticipatory—there is no way to choose thei-th sign without knowledge of v j forj>i.

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References

  1. [1]

    I. Bárány andV. S. Grünberg, On some combinatorial questions in finite-dimensional spaces,Linear Algebra and its Applications,41 (1981), 1–9.

    MATH  Article  MathSciNet  Google Scholar 

  2. [2]

    J. Spencer, Balancing Games,J. Combinatorial Th., Ser B,23 (1977), 68–74.

    MATH  Article  Google Scholar 

  3. [3]

    J. Spencer, Six Standard Deviations Suffice,Trans. Amer. Math. Soc.,289 (1985), 679–705.

    MATH  Article  MathSciNet  Google Scholar 

  4. [4]

    M. Klawe, Optimal Strategies for a Fair Betting Game,Disc. Appl. Math.,1 (1979), 105–115.

    MATH  Article  MathSciNet  Google Scholar 

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Spencer, J. Balancing vectors in the max norm. Combinatorica 6, 55–65 (1986). https://doi.org/10.1007/BF02579409

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AMS subject classification (1980)

  • 05 B 20