### 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 language | English (US) |
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Pages (from-to) | 299-304 |

Number of pages | 6 |

Journal | Combinatorica |

Volume | 3 |

Issue number | 3-4 |

DOIs | |

State | Published - Sep 1983 |

### Fingerprint

### Keywords

- AMS subject classification (1980): 05B20

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Mathematics(all)

### Cite this

*Combinatorica*,

*3*(3-4), 299-304. https://doi.org/10.1007/BF02579185

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

Research output: Contribution to journal › Article

*Combinatorica*, vol. 3, no. 3-4, pp. 299-304. https://doi.org/10.1007/BF02579185

}

TY - JOUR

T1 - Balancing matrices with line shifts

AU - Beck, József

AU - Spencer, Joel

PY - 1983/9

Y1 - 1983/9

N2 - 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.

AB - 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.

KW - AMS subject classification (1980): 05B20

UR - http://www.scopus.com/inward/record.url?scp=51649161116&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=51649161116&partnerID=8YFLogxK

U2 - 10.1007/BF02579185

DO - 10.1007/BF02579185

M3 - Article

VL - 3

SP - 299

EP - 304

JO - Combinatorica

JF - Combinatorica

SN - 0209-9683

IS - 3-4

ER -