Minimizing the weight of the union-closure of families of two-sets
نویسندگان
چکیده
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 number of distinct 2-sets. 68 U. LECK, I.T. ROBERTS AND J. SIMPSON
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ورودعنوان ژورنال:
- Australasian J. Combinatorics
دوره 52 شماره
صفحات -
تاریخ انتشار 2012