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.
|Number of pages||7|
|Journal||Australasian Journal of Combinatorics|
|Publication status||Published - 2012|