Yet two additional large numbers of subuniverses of finite lattices
Delbrin Ahmed, Eszter K. Horváth · Discussiones Mathematicae - General Algebra and Applications · 2019
By a subuniverse, we mean a sublattice or the emptyset. We prove that the fourth largest number of subuniverses of an n-element lattice is 43 2n−6 for n ≥ 6, and the fifth largest number of subuniverses of an n-element lattice is 85 2n−7 for n ≥ 7. Also, we describe the n-element lattices with exactly 43 2n−6 (for n ≥ 6) and 85 2n−7 (for n ≥ 7) subuniverses.