  Catalan words are particular growth-restricted words counted by the eponymous
integer sequence. In this article we consider Catalan words avoiding a pair of
patterns of length 3, pursuing the recent initiating work of the first and last
authors and of S. Kirgizov where (among other things) the enumeration of
Catalan words avoiding a patterns of length 3 is completed. More precisely, we
explore systematically the structural properties of the sets of words under
consideration and give enumerating results by means of recursive decomposition,
constructive bijections or bivariate generating functions with respect to the
length and descent number. Some of the obtained enumerating sequences are
known, and thus the corresponding results establish new combinatorial
interpretations for them.
