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

@article{Leck2012MinimizingTW,
  title={Minimizing the weight of the union-closure of families of two-sets},
  author={Uwe Leck and Ian T. Roberts and Jamie Simpson},
  journal={Australasian J. Combinatorics},
  year={2012},
  volume={52},
  pages={67-74}
}
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 wi with wi ≤ wi+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… CONTINUE READING

Citations

Publications citing this paper.
Showing 1-4 of 4 extracted citations

Two extremal problems related to orders

J. Comb. Optim. • 2018
View 10 Excerpts
Highly Influenced

The Journey of the Union-Closed Sets Conjecture

Graphs and Combinatorics • 2015
View 7 Excerpts
Method Support
Highly Influenced

Inequalities for cross-unions of collections of finite sets

Eur. J. Comb. • 2014
View 3 Excerpts
Highly Influenced

References

Publications referenced by this paper.
Showing 1-4 of 4 references

Extremal Problems and Designs on Finite Sets

I. T. Roberts
PhD Thesis, • 1999
View 3 Excerpts
Highly Influenced

A note on the union-closed sets conjecture

Australasian J. Combinatorics • 2010
View 1 Excerpt

On the union-closed sets conjecture

D. G. Sarvate, J.-C. Renaud
Ars Combin • 1989
View 1 Excerpt