Delbrin Ahmed – Some large numbers of subuniverses of latices and semilattices

Szeged University, Bolyai Institute

We prove that the first largest number of subuniverses of an -element semilattice is while the second largest number is
and the third one is
Also, we describe the -element semilattices with exactly ,
or
subuniverses. Moreover, we prove that the fourth largest number of subuniverses of an -element lattice is
, and the fifth largest number is
. Also, we describe the -element lattices with exactly
and
subuniverses.