Slim semimodular lattices. I. A visual approach (Q1757868)

Planar lattices have a diagram to be depicted in the plane. This nice paper under review proves this approach to be very appropriate for finite semimodular lattices which are slim, i.e., do not admit any 3-element antichain of join irreducibles. The first main result shows that any such lattice can be obtained from chains by iterative extensions of a very simple kind (adding `corners' and `forks', respectively); the second one shows that any such lattice can be obtained from the product of two chains by first adding forks and then deleting corners.