Yet Two Additional Large Numbers of Subuniverses of Finite Lattices

Abstract

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.

Keywords

• finite lattice
• sublattice
• number of sublattices
• subuniverse
• primary: 06b99
• secondary: 08a30