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A note on lattices with many sublattices

A note on lattices with many sublattices

For every natural number n 5, we prove that the number of subuniverses of an nelement lattice is 2 n , 13 2 n 4 , 23 2 n 5 , or less than 23 2 n 5 .Also, we describe the n-element lattices with exactly 2 n , 13 …