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Resolvable coverings. (English) Zbl 0801.05020
Summary: A minimum covering of pairs by triples in a $$6n$$-element set contains $$6n^ 2$$ triples. Can such a covering be resolvable? A. Assaf, E. Mendelsohn and D. R. Stinson [Util. Math. 32, 67-74 (1987; Zbl 0649.05024)] showed that this is not possible for $$n<3$$, and that for $$n\geq 3$$ such a resolvable covering exists if $$n\not\in \{6,7,8,10,1,13,14,17,22\}$$. In the present paper, we show that such resolvable coverings exist for these nine values of $$n$$.

##### MSC:
 05B40 Combinatorial aspects of packing and covering
##### Keywords:
triples; resolvable coverings