### Abstract

Let a be a column of the m × n matrix M and A a set of its columns. We say that A implies a iff M contains no two rows equal in A but different in a. It is easy to see that if ℳ_{M}(A) denotes the columns implied by A, than ℳ_{M}(A) is a closure operation. We say that M represents this closure operation. s() is the minimum number of the rows of the matrices representing a given closure operation. s(ℳ) is determined for some particular closure operations.

Original language | English |
---|---|

Pages (from-to) | 115-128 |

Number of pages | 14 |

Journal | Discrete Applied Mathematics |

Volume | 11 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1985 |

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### ASJC Scopus subject areas

- Computational Theory and Mathematics
- Applied Mathematics
- Discrete Mathematics and Combinatorics
- Theoretical Computer Science

### Cite this

*Discrete Applied Mathematics*,

*11*(2), 115-128. https://doi.org/10.1016/S0166-218X(85)80003-2

**Minimum matrix representation of closure operations.** / Demetrovics, J.; Füredi, Z.; Katona, G. O H.

Research output: Contribution to journal › Article

*Discrete Applied Mathematics*, vol. 11, no. 2, pp. 115-128. https://doi.org/10.1016/S0166-218X(85)80003-2

}

TY - JOUR

T1 - Minimum matrix representation of closure operations

AU - Demetrovics, J.

AU - Füredi, Z.

AU - Katona, G. O H

PY - 1985

Y1 - 1985

N2 - Let a be a column of the m × n matrix M and A a set of its columns. We say that A implies a iff M contains no two rows equal in A but different in a. It is easy to see that if ℳM(A) denotes the columns implied by A, than ℳM(A) is a closure operation. We say that M represents this closure operation. s() is the minimum number of the rows of the matrices representing a given closure operation. s(ℳ) is determined for some particular closure operations.

AB - Let a be a column of the m × n matrix M and A a set of its columns. We say that A implies a iff M contains no two rows equal in A but different in a. It is easy to see that if ℳM(A) denotes the columns implied by A, than ℳM(A) is a closure operation. We say that M represents this closure operation. s() is the minimum number of the rows of the matrices representing a given closure operation. s(ℳ) is determined for some particular closure operations.

UR - http://www.scopus.com/inward/record.url?scp=0022076473&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0022076473&partnerID=8YFLogxK

U2 - 10.1016/S0166-218X(85)80003-2

DO - 10.1016/S0166-218X(85)80003-2

M3 - Article

AN - SCOPUS:0022076473

VL - 11

SP - 115

EP - 128

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

SN - 0166-218X

IS - 2

ER -