Balancing vectors in the max norm

J. Spencer

Research output: Contribution to journalArticlepeer-review


Let v1, ..., v n be vectors in R 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 most Kn 1/2. It is further shown that such a choice of signs must be anticipatory-there is no way to choose the i-th sign without knowledge of v j for j>i.

Original languageEnglish (US)
Pages (from-to)55-65
Number of pages11
Issue number1
StatePublished - Mar 1986


  • AMS subject classification (1980): 05B20

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Computational Mathematics


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