MMN-2821
A note on lattices with many sublattices
Gábor Czédli; Eszter K. Horváth;Abstract
For every natural number $n\geq 5$, we prove that the number of
subuniverses of an $n$-element lattice is $2^n$,
$13\cdot 2^{n-4}$, $23\cdot 2^{n-5}$, or less than $23\cdot 2^{n-5}$. By a subuniverse, we mean a sublattice or the emptyset.
Also, we describe the $n$-element lattices with exactly $2^n$,
$13\cdot 2^{n-4}$, or $23\cdot 2^{n-5}$ subuniverses.
Vol. 20 (2019), No. 2, pp. 839-848