Yet Two Additional Large Numbers of Subuniverses of Finite Lattices

Delbrin Ahmed 1  and Eszter K. Horváth 1
  • 1 University of Szeged

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.

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