Geodesic
Yet Two Additional Large Numbers of Subuniverses of Finite Lattices
Discussiones Mathematicae. General Algebra and Applications, Tome 39 (2019) no. 2, pp. 251-261.

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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 
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Ahmed, Delbrin; Horváth, Eszter K. Yet Two Additional Large Numbers of Subuniverses of Finite Lattices. Discussiones Mathematicae. General Algebra and Applications, Tome 39 (2019) no. 2, pp. 251-261. http://geodesic.mathdoc.fr/item/DMGAA_2019_39_2_a6/

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