Balancing matrices with line shifts

József Beck, Joel Spencer

Research output: Contribution to journalArticle

Abstract

We give a purely deterministic proof of the following theorem of J. Komlós and M. Sulyok. Let A=(a ij ), a ij =±1 be an n×n matrix. One can multiply some rows and columns by -1 such that the absolute value of the sum of the elements of the matrix is ≦2 if n is even and 1 if n is odd. Note that Komlós and Sulyok applied probabilistic ideas and so their method worked only for n>n 0.

Original languageEnglish (US)
Pages (from-to)299-304
Number of pages6
JournalCombinatorica
Volume3
Issue number3-4
DOIs
StatePublished - Sep 1983

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Balancing
Line
Absolute value
Multiplication
Odd
Theorem

Keywords

  • AMS subject classification (1980): 05B20

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Mathematics(all)

Cite this

Balancing matrices with line shifts. / Beck, József; Spencer, Joel.

In: Combinatorica, Vol. 3, No. 3-4, 09.1983, p. 299-304.

Research output: Contribution to journalArticle

Beck, József ; Spencer, Joel. / Balancing matrices with line shifts. In: Combinatorica. 1983 ; Vol. 3, No. 3-4. pp. 299-304.
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