For every natural number n≥5, we prove that the number of subuniverses
of an n-element lattice is 2n, 13⋅2n−4, 23⋅2n−5, or
less than 23⋅2n−5. By a subuniverse, we mean a sublattice or the
emptyset. Also, we describe the n-element lattices with exactly 2n,
13⋅2n−4, or 23⋅2n−5 subuniverses.Comment: 10 pages and 4 figure