  We define the notion of a Catalan pair (which is a pair of binary relations
(S,R) satisfying certain axioms) with the aim of giving a common language to
most of the combinatorial interpretations of Catalan numbers. We show, in
particular, that the second component R uniquely determines the pair, and we
give a characterization of R in terms of forbidden configurations. We also
propose some generalizations of Catalan pairs arising from some slight
modifications of (some of the) axioms.
