### Abstract

_{n}|/2

^{n}|, where B

_{n}denotes the power set of [n]. Besides, the problem of minimizing |F∨G|over all union-closed FF and G∨G generated by a given number

*r*of singletons and a given number s > (r 2) of two-sets, respectively, is solved.

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

Pages (from-to) | 392-401 |

Number of pages | 10 |

Journal | European Journal of Combinatorics |

Volume | 35 |

DOIs | |

Publication status | Published - 2014 |

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### Cite this

*European Journal of Combinatorics*,

*35*, 392-401. https://doi.org/10.1016/j.ejc.2013.06.036

}

*European Journal of Combinatorics*, vol. 35, pp. 392-401. https://doi.org/10.1016/j.ejc.2013.06.036

**Inequalities for cross-unions of collections of finite sets.** / Leck, Uwe; Roberts, Ian.

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

TY - JOUR

T1 - Inequalities for cross-unions of collections of finite sets

AU - Leck, Uwe

AU - Roberts, Ian

PY - 2014

Y1 - 2014

N2 - Some inequalities for cross-unions of families of finite sets are proved that are related to the problem of minimizing the union-closure of a uniform family of given size. The cross-union of two families F and G of subsets of [n]={1,2,…,n}[n]={1,2,…,n} is the family F∨G={F∪G:F∈F,G∈G}. It is shown that |F∨G|/|F|≥|G∨Bn|/2n|, where Bn denotes the power set of [n]. Besides, the problem of minimizing |F∨G|over all union-closed FF and G∨G generated by a given number r of singletons and a given number s > (r 2) of two-sets, respectively, is solved.

AB - Some inequalities for cross-unions of families of finite sets are proved that are related to the problem of minimizing the union-closure of a uniform family of given size. The cross-union of two families F and G of subsets of [n]={1,2,…,n}[n]={1,2,…,n} is the family F∨G={F∪G:F∈F,G∈G}. It is shown that |F∨G|/|F|≥|G∨Bn|/2n|, where Bn denotes the power set of [n]. Besides, the problem of minimizing |F∨G|over all union-closed FF and G∨G generated by a given number r of singletons and a given number s > (r 2) of two-sets, respectively, is solved.

U2 - 10.1016/j.ejc.2013.06.036

DO - 10.1016/j.ejc.2013.06.036

M3 - Article

VL - 35

SP - 392

EP - 401

JO - European Journal of Combinatorics

JF - European Journal of Combinatorics

SN - 0195-6698

ER -