I don't know if there is any better terminology but such families of sets (either disjoint or containing one another) are said to form a Laminar family or a hierarchical system. There is a bijection between Laminar families from a set S and S-rooted forests. If a laminar family has the additional property that each element in S is contained in at least one member of the family then one calls it a complete laminar family. The enumeration of laminar families is open.
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I don't know if there is any better terminology but such families of sets (either disjoint or containing one another) are said to form a Laminar family or a hierarchical system. |
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