On Tamari lattices

Abstract Tamari lattices are defined as the set of all binary bracketings on a fixed number of symbols ordered by applying the associativity rule only in one direction. Using methods of formal concept analysis we derive a recursive construction of these lattices based on successive doublings of intervals. It turns out that for every n ϵ N Tamari lattices and their congruence lattices have the same number of elements and the same number of coverings, both connected with the Catalan numbers.