The asymptotic number of planar, slim, semimodular lattice diagrams
  A lattice L is slim if it is finite and the set of its join-irreducible elements contains no three-element antichain. We prove that there exists a positive constant C such that, up to similarity, the number of planar diagrams of these lattices of size n is asymptotically C times 2 to the n. 
G\'abor Cz\'edli
math.RA