Congruence lattices of planar lattices (Q1207370)

The main result is the following: Let \(D\) be a finite distributive lattice with more than one element. Then there exists a finite planar lattice \(L\) with no proper automorphism such that the congruence lattice of \(L\) is isomorphic to \(D\); the lattice \(L\) can be chosen to have \(O(| J|^ 3)\) elements, where \(J\) is the set of nonzero join- irreducible elments in \(D\).