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

Leck, Uwe, Roberts, Ian T. and Simpson, Jamie (2012). Minimizing the weight of the union-closure of families of two-sets. Australasian Journal of Combinatorics,52(1):67-73.

Document type: Journal Article
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IRMA ID 82794376xPUB69
Title Minimizing the weight of the union-closure of families of two-sets
Author Leck, Uwe
Roberts, Ian T.
Simpson, Jamie
Journal Name Australasian Journal of Combinatorics
Publication Date 2012
Volume Number 52
Issue Number 1
ISSN 1034-4942   (check CDU catalogue open catalogue search in new window)
Scopus ID 2-s2.0-84856248689
Start Page 67
End Page 73
Total Pages 6
Place of Publication Australia
Publisher Centre for Discrete Mathematics & Computing
HERDC Category C1 - Journal Article (DIISR)
Abstract It is proved that, for any positive integer m, the weight of the union-closure 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.
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