On the Number of Covering Pairs in Speciied Lattices

Given a class F of posets, let ex(F; n) denote the maximum number of covering pairs achieved by an n-element poset in F. We determine this number for the class of N-free lattices and give crude lower and upper bounds for the classes of distributive and covering lattices. The structural characterization of covering lattices leads us to a class of lattices whose elements have a bounded number of lower or upper covers. This class satisses a conjecture of Bollobas and Rival, who originally ask for ex(L; n) where L denotes the class of all lattices.