Abstract
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.
| 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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Cite this
Leck, U., Roberts, I., & Simpson, J. (2012). Minimizing the weight of the union-closure of families of two-sets. Australasian Journal of Combinatorics, 52(1), 67-73.