An (n, k, l) covering design is a family of k-subsets of an n-element set such that every l-subset is contained in at least one of them. Now, what is the correct term for a family of k-subsets such that every l-subset contains one.
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$\begingroup$ It's the complement of an n-k,n-l covering design. $\endgroup$– The Masked AvengerMar 7, 2015 at 15:43
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1$\begingroup$ That's right, although I suspect the OP knows this already. Regarding naming, I think co-covering is not a bad term. But design theory already has a proliferation of special terms, so it's maybe best to complement parameters as stated above. $\endgroup$– Peter DukesJul 21, 2015 at 23:19
4 Answers
You may be thinking of Packing Designs. They solve the problem of the largest set of $k$-sets none of which contain the same $l$-set.
In topology or set theory or in the Birkhoff lattice theory with $0$ and $1$, where covering means a collection such that the union is the total space (or total set or 1), the dual notion is a collection with the empty intersection (or $0$). Years ago I have introduced for such a dual notion the name ver.
Perhaps, in the situation as above, perhaps name ver is still optimal, despite the overloading it.
Thus, after all, the name should be:
$$\mathbf{ver}$$
Simple.
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$\begingroup$ It goes without saying that the dual to ver is cover. $\endgroup$ Sep 11, 2016 at 4:29