### Abstract

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

Pages (from-to) | 67-73 |

Number of pages | 7 |

Journal | Australasian Journal of Combinatorics |

Volume | 52 |

Issue number | 1 |

Publication status | Published - 2012 |

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*Australasian Journal of Combinatorics*,

*52*(1), 67-73.

}

*Australasian Journal of Combinatorics*, vol. 52, no. 1, pp. 67-73.

**Minimizing the weight of the union-closure of families of two-sets.** / Leck, Uwe; Roberts, Ian; Simpson, Jamie.

Research output: Contribution to journal › Article › Research › peer-review

TY - JOUR

T1 - Minimizing the weight of the union-closure of families of two-sets

AU - Leck, Uwe

AU - Roberts, Ian

AU - Simpson, Jamie

PY - 2012

Y1 - 2012

N2 - It is proved that, for any positive integer m, the weight of the unionclosure of any m distinct 2-sets is at least as large as the weight of the union-closure of the first m 2-sets in squashed (antilexicographic) order, where all i-sets have the same non-negative weight w i with w i ? w i+1 for all i, and the weight of a family of sets is the sum of the weights of its members. As special cases, solutions are obtained for the problems of minimising size and volume of the union-closure of a given number of distinct 2-sets.

AB - It is proved that, for any positive integer m, the weight of the unionclosure of any m distinct 2-sets is at least as large as the weight of the union-closure of the first m 2-sets in squashed (antilexicographic) order, where all i-sets have the same non-negative weight w i with w i ? w i+1 for all i, and the weight of a family of sets is the sum of the weights of its members. As special cases, solutions are obtained for the problems of minimising size and volume of the union-closure of a given number of distinct 2-sets.

UR - https://ajc.maths.uq.edu.au/?page=get_volumes&volume=52

M3 - Article

VL - 52

SP - 67

EP - 73

JO - Australasian Journal of Combinatorics

JF - Australasian Journal of Combinatorics

SN - 1034-4942

IS - 1

ER -