Abstract
| 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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Minimizing the weight of the union-closure of families of two-sets. / Leck, Uwe; Roberts, Ian; Simpson, Jamie.
In: Australasian Journal of Combinatorics, Vol. 52, No. 1, 2012, p. 67-73.Research output: Contribution to journal › Article › Research › peer-review
TY - JOUR
T1 - Minimizing the weight of the union-closure of families of two-sets
AU - Leck, Uwe
AU - Roberts, Ian
AU - Simpson, Jamie
PY - 2012
Y1 - 2012
N2 - 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.
AB - 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.
UR - https://ajc.maths.uq.edu.au/?page=get_volumes&volume=52
M3 - Article
VL - 52
SP - 67
EP - 73
JO - Australasian Journal of Combinatorics
JF - Australasian Journal of Combinatorics
SN - 1034-4942
IS - 1
ER -