Congruence lattices of small planar lattices
George Grätzer, H. Lakser, E. T. Schmidt · Proceedings of the American Mathematical Society · 1995
For a finite distributive lattice D with n join-irreducible elements, we construct a finite (planar) lattice L with O ( n 2 ) O({n^2}) elements such that the congruence lattice of L is isomorphic to D . This improves on an early result of R. P. Dilworth (around 1940) and G. Grätzer and E. T. Schmidt (1962) constructing such a (nonplanar) lattice L with O ( 2 2 n ) O({2^{2n}}) elements, and on a recent construction of G. Grätzer and H. Lakser which yields a finite (planar) lattice L with O ( n 3 ) O({n^3}) elements.