If  are sets such that no one is contained in another, then there is an associated lattice on  corresponding to inclusion relations among unions of the sets. Two lattices on  are equivalent if there is a permutation of  under which they correspond. We show that for  and 4, there are 1, 1, 4, and 50 equivalence classes of lattices on  obtained from sets in this way. We cannot find a reference to previous work on this enumeration problem in the literature, and so wish to introduce it for subsequent investigation. We explain how the problem arose from algebraic topology.

enumeration, lattice, Stanley-Reisner ring.