Balanced two-colorings of finite sets in the square I

József Beck

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37 Scopus citations


Let T(N) be the least integer such that one can assign ± 1's to any N points in the unit square so that the sum of these values in any rectangle with sides parallel to those of the square have absolute value at most T(N). G. Tusnádi asked what could be said about the order of magnitude of T(N). We prove {Mathematical expression} In contrast, if T*(N) denotes the corresponding quantity where rectangles of any possible orientation are considered, we have {Mathematical expression} for any ε > 0.

Original languageEnglish (US)
Pages (from-to)327-335
Number of pages9
Issue number4
StatePublished - Dec 1981
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Discrete Mathematics and Combinatorics
  • Computational Mathematics


  • AMS subject classification (1980): 10K30, 10H20, 05C55


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