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

Uwe Leck, Ian Roberts, Jamie Simpson

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    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 languageEnglish
    Pages (from-to)67-73
    Number of pages7
    JournalAustralasian Journal of Combinatorics
    Volume52
    Issue number1
    Publication statusPublished - 2012

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