Catalan words avoiding pairs of length three patterns

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